“Rock of Ages” is by the Reverend Augustus Montague Toplady written in 1763 and first published in The Gospel Magazine in 1775.

Traditionally, it is held that Toplady drew his inspiration from an incident in the gorge of Burrington Combe in the Mendip Hills in England. Toplady, a preacher in the nearby village of Blagdon, was travelling along the gorge when he was caught in a storm. Finding shelter in a gap in the gorge, he was struck by the title and scribbled down the initial lyrics on a playing card.
Meaning of by Jonathan Aubuchon…

Verse 1:

Rock of Ages, cleft for me,

Let me hide myself in Thee;

Let the water and the blood,

From Thy wounded side which flowed,

Be of sin the double cure,

Save from wrath and make me pure.

Jesus Christ is the Rock of Ages who was cleft for us, in whom we can hide, and from whom we receive the living water: 1 Cor. 10.1-4
As the rock who was cleft for us, blood and water flowed from His wounded side: Jn. 19.33-34
This sacrificial death of Christ is of sin the double cure; The blood of Christ is able both to forgive us of our sins and then to break sin’s power that we might be kept pure: Rom. 6.7-9
Verse 2:

Not the labors of my hands, Can fulfill thy law’s commands

Could my zeal no respite know, Could my tears forever flow

All for sin could not atone, Thou must save and Thou alone

The labor of our hands can never fulfill the law’s demands because we simply cannot do enough good works to atone for our sins: Tit. 3.5
Thus, we must look to God for the grace that we need to be saved: Eph. 2.8-9
Certainly, we need to have tears for sin and zeal that knows no respite (or rest) in coming to and serving Christ: 2 Cor. 7.10, Rev. 3.19
However, we cannot atone for our sin; Christ alone is the living stone to whom we must come for salvation: 1 Pet. 2.4-10
Verse 3:

Nothing in my hands I bring, Simply to the cross I cling

Naked, come to thee for dress, Helpless, look to thee for grace

Foul, I to the fountain fly, Wash me, Savior, or I die

There is no price that we can bring; we can only cling to the cross because it represents God’s means to save us: 1 Cor. 1.18-21
Because we are foul (or vile), we must in our helplessness look to Christ as the fountain to wash away sins or we shall surely die, just as the Psalmist looked to the Lord as His rock of refuge: Ps. 31.1-2
Verse 4:

While I draw this fleeting breath,

when mine eyes shall close in death.

When I soar to worlds unknown,

See Thee on Thy judgment throne,

Rock of Ages, cleft for me, Let me hide myself in Thee.

Someday we shall cease to draw this fleeting breath, and then our eyes shall close in death: Heb. 9.27
After that, we shall soar to worlds unknown and eventually behold Christ on His throne. But Jesus Himself said that when He comes He will sit on His throne of judgment: Matt. 25.31
And when we stand before Him, we can praise Him as the Rock of Ages who will redeem us eternally: Ps. 78.35.

Ex 33
17 And the LORD said to Moses, “This very thing that you have spoken I will do, for you have found favor in my sight, and I know you by name.”
18 Moses said, “Please show me your glory.”
19 And he said, “I will make all my goodness pass before you and will proclaim before you my name ‘The LORD.’ And I will be gracious to whom I will be gracious, and will show mercy on whom I will show mercy.
20 But,” he said, “you cannot see my face, for man shall not see me and live.”
21 And the LORD said, “Behold, there is a place by me where you shall stand on the rock,
22 and while my glory passes by I will put you in a cleft of the rock, and I will cover you with my hand until I have passed by.
23 Then I will take away my hand, and you shall see my back, but my face shall not be seen.”