This is the dead land This is cactus land Here the stone images Are raised, here they receive The supplication of a dead man's hand Under the twinkle of a fading star.
The Hollow Men live in a region that looks like desert where nothing lives but cacti that can survive without much water.
The Hollow Men pray to "stone images," which are like false gods or idols. The "dead man" is one of the Hollow Men. They are dead in the sense that they do not have life, but they also cannot cross over into the kingdom of death.
It's like being trapped at a rest stop on the highway between two destinations.
To "supplicate" is to beg or ask for something, so the Hollow Men are begging the stones to help them out of their mess.
The star might represent hope or salvation, as stars are usually associated with Heaven. But their hopes are fading fast, and only a small "twinkle" of light remains.
Is it like this In death's other kingdom Waking alone At the hour when we are Trembling with tenderness Lips that would kiss Form prayers to broken stone.
All of a sudden the Hollow Men are curious about "death's other Kingdom."
They don't really suspect that things are better in Heaven or anywhere else. Otherwise, they probably would have tried to get there.
They want to know if people in the other kingdom also wake up alone, with warm and tender feelings but no outlet for them except to pray to a bunch of "broken stone" images.
If you have read Shakespeare's Romeo and Juliet, you might notice that these lines reverse Juliet's claim that saints must use their lips for prayer rather than kissing. The Hollow Men pray, but their prayers are blasphemous and corrupted:
ROMEO Have not saints lips, and holy palmers too? JULIET Ay, pilgrim, lips that they must use in prayer.