So what's the significance of this line from The Waste Land?

I don't know. Here are a few thoughts and questions I have about it:

Obviously, this is something about seeking or offering shelter. Shelter for whom? Shelter from what?

How does this line relate to What the Thunder Said, in which Eliot writes:

Here is no water but only rock
Rock and no water and the sandy road
The road winding above among the mountains
Which are mountains of rock without water
If there were water we should stop and drink
Amongst the rock one cannot stop or think

Is there a connection between the two references to rock?

Here's what I think. The rock represents someone in Eliot's life, as do the hyacinth girl and the drowned sailor. This is someone hard, tough, stoic - but the tradeoff is that there is no way to get past the shell. One cannot stop and drink in his personality; the rock prevents it. He can offer shelter, but not sustenance.

That's my take on it, anyway.

This line also alludes to another of Eliot's poems, "The Death of Saint Narcissus" which reads

Come under the shadow of this gray rock -
Come in under the shadow of this gray rock,
And I will show you something different from either
Your shadow sprawling over the sand at daybreak, or
Your shadow leaping behind the fire against the red rock:
I will show you his bloody cloth and limbs
And the gray shadow on his lips.

I have also heard this is a Biblical allusion to Isaiah 32:1-2 where the coming of the Messiah will be "as the shadow of a great rock in a weary land."
