Most of this great poem is a dramatic monologue, in which the narrator delivers an extended reflection on a topic. At some points, though, it slips into stream of consciousness.
In stream of consciousness writing, writers try to portray the way thoughts move through a person's mind. These thoughts tumble one after another, and the mind sometimes jumps from topic to topic in ways that are normal within the mind but uncommon in daily conversation.
In "Prufrock," you can see several examples of stream of consciousness.
Consider this brief stanza:
"In the room the women come and go
Talking of Michelangelo."
The first time it occurs in the poem, it is possible the narrator actually saw women walking in and out, and that's what they were talking about. However, when the same lines recur later, it is more likely they are bits of memory that drift in, as the narrator is reminded of something.
After the second time that couplet occurs, you'll find these lines:
"And indeed there will be time
To wonder, “Do I dare?” and, “Do I dare?”
Time to turn back and descend the stair,
With a bald spot in the middle of my hair —
(They will say: “How his hair is growing thin!”)"
That sudden moment of self-consciousness, and that image of hair going thin, is the same kind of self-conscious intrusion that is a common element in stream of consciousness.