The following is from Keil & Delitzsch "Commentary on the Old Testament," volume 5: "Psalms" (1867)--Hebrew manuscripts are used including Hebrew numbering of verses. It's interesting to note that all the Psalms have names. I'm going to have to skip a fair amount in the commentary as I don't read Hebrew and there is no transliteration. Anything in brackets is what I have added.
The occasion of this Psalm is a thunderstorm; it is not, however, limited to the outward natural phenomena, but therein is perceived the self-attestation of the God of the redemptive history. Just as in the second part of Psalm 19, the God of the revelation of salvation is called Jahve seven times in distinction from the God revealed in nature, so in this a Psalm of thunders voice of is repeated seven times, so that it may be called the Psalm of the seven thunders (Apoc. 10:3 sq.). During the time of the second Temple, as the addition to the inscription by the LXX seems to imply,* it was sung on the Shemini Azereth, the last day (Lev 23:36) of the feast of tabernacles. Between two testrastichs, in each of which the name Jahve occurs four times, lie three pentastichs, which, in their sevenfold voicings of, represent the peals of thunder which follow in rapid succession as the storm increases in its fury.
Vers. 1-2. The opening strophe calls upon the celestial spirits to praise Jahve; for a revelation of divine glory is in preparation, which, in its first movements, they are accounted worthy to behold, for the roots of everything that takes place in this world are in the invisible world. It is not the mighty of the earth, but the angels that are here [spoken of]. A revelation of the power of God is near at hand. The heavenly spirits are to prepare themselves for it with all the outward display of which they are capable. If verse 2 were a summons to the church on earth, or, as in 96:9, to the dwellers upon the earth, then there ought to be some expression to indicate the change in the parties addressed; it is, therefore, in verse 2 as in verse 1, directed to the priests of the heavenly temple. In the Apocalypse, also, the songs of praise and trumpeting of the angels precede the judgments of God.
Vers. 3-9. Now follows the description of the revelation of God's power, which is the ground of the summons, and is to be the subject-matter of their praise. The All-glorious One makes Himself heard in the language of the thunder, and reveals Himself in the storm. The waters in verse 3 are not the lower waters. Then the question arises what are they? Were the waters of the Mediterranean intended, they would be more definitely denoted in such a vivid description. It is, however, far more appropriate to the commencement of this description to understand them to mean the mass of water gathered together in the thick, black storm-clouds. The rumblings of Jahve is, as the poet himself explains in verse 3b, the thunder produced on high which rolls over the sea of waters floating above the earth in the sky. The rumbling of Jahve is, issues forth, or passes by. In verse 3 the first peals of thunder are heard; in verse 4 the storm is coming nearer, and the peals become stronger, and now it bursts forth with its full violence: amidst the rolling of the thunder the descending lightning flashes rive the cedars of Lebanon (as is well-known, the lightning takes the outermost points). The suffix in verse 6a does not refer proleptically to the mountains mentioned afterwards, but naturally to the cedars, which bend down before the storm and quickly rise up again. The skipping of Lebanon and Sirion, however, is not to be referred to the fact, that their wooded summits bend down and rise again, but, according to 114:4, to their being shaken by the crash of the thunder,--a feature in the picture which certainly does not rest upon what is actually true in nature, but figuratively describes the apparent quaking of the earth during a heavy thunderstorm. The lightning makes these mountains bound like young antelopes [the KJV has the word "unicorn" here].
Each peal of thunder is immediately followed by a flash of lightning; Jahve's thunder cleaveth flames of fire, i.e. forms the fire-matter of the storm-clouds into cloven flames of fire, into lightnings that pass swiftly along [depictions of Pentecost?]. The brevity and threefold division of verse 7 depicts the incessant, zigzag, quivering movement of the lightning. From the northern mountains the storm sweeps on towards the south of Palestine into the Arabian desert, viz. as we are told in verse 8b, the wilderness region of Kadesh (Kadesh Barnea), which, however we may define its position, must certainly have lain near the steep western slope of the mountains of Edom toward the Arabah. Jahve's thunder, viz. the thunderstorm, puts this desert in a state of whirl, inasmuch as it drives the sand before it in whirlwinds; and among the mountains it, viz. the strong lightning and thundering, makes the hinds to writhe, inasmuch as from fright they bring forth prematurely. The poet describes the effect of the storm which "shells" the woods, inasmuch as it beats down the branches of the trees, both the tops and the foliage. While Jahve thus reveals Himself from heaven upon the earth in all His irresistible power, His heavenly palace, i.e. each of the beings therein, says: Glory! That which the poet, in verses 1 and 2, has called upon them to do, now takes place. Jahve receives back His glory, which is immanent in the universe, in the thousand-voiced echo of adoration.
Vers. 10-11. The poet has not thus far expressly referred to the torrents of rain, in which the storm empties itself. The word flood [mabbuwl] occurs exclusively in Genesis 6-11 as the name of the great Flood. Every tempest, however, calls to mind this judgment and its merciful issue, for it comes before us in sacred history as the first appearance of rain with lightning and thunder, and of the bow in the clouds speaking its message of peace. Jahve--says the poet--sat (upon His throne) at the Flood (to execute it), and sits (enthroned) in consequence thereof, or since that time, as this present revelation of Him in the tempest shews, as King for ever, inasmuch as He rules down here upon earth from His throne in the heavens (115:16) in wrath and in mercy, judging and dispensing blessing. Here upon earth He has a people, whom from above He endows with a share of His own might and blesses with peace, while the tempests of His wrath burst over their foes. How expressive is "peace" as the closing word of this particular Psalm! It spans the Psalm like a rain-bow. The opening of the Psalm shews us the heavens opened and the throne of God in the midst of the angelic songs of praise, and the close of the Psalm shews us, on earth, His people victorious and blessed with peace, in the midst of Jahve's voice of anger, which shakes all things.
In the Vulgate Latin version is added, "at the finishing of the tabernacle"; suggesting that this psalm was composed at that time, and on that occasion; not at the finishing of the tabernacle by Moses, but at the finishing of the tent or tabernacle which David made for the ark in Zion, (2 Sam 6:17). The title in the Arabic version is, "a prophecy concerning the incarnation, ark, and tabernacle." In the Septuagint version, from whence the Vulgate seems to have taken the clause, it is, at the "exodion," "exit," or "going out of the tabernacle"; that is, of the feast of tabernacles; and the eighth day...
(The New John Gill's Exposition of the Entire Bible)
From The Legends of the Jews, Louis Ginzberg:
These words as well as the others, made know by God on Mount Sinai, were not heard by Israel alone, but by the inhabitants of all the earth. The Divine voice divided itself into the seventy tongues of men, so that all might understand it; but whereas Israel could listen to the voice without suffering harm, the souls of the heathens almost fled from them when they heard it.  When the Divine voice sounded, all the dead in Sheol were revived, and betook themselves to Sinai; for the revelation took place in the presence of the living as well as of the dead, yea, even the souls of those who were not yet born were present. Every prophet, every sage, received at Sinai his share of the revelation, which in the course of history was announced by them to mankind. All heard indeed the same words, but the same voice, corresponding to the individuality of each, was God's way of speaking with them. And as the same voice sounded differently to each one, so did the Divine vision appear differently to each, wherefore God warned them not to ascribe the various forms to various beings, saying: "Do not believe that because you have seen Me in various forms, there are various gods, I am the same that appeared to you at the Red Sea as a God of war, and at Sinai as a teacher."