In this poem, daily life is a strain and a drag for Prufrock. He expresses frustration in the daily routines, and in how meaningless it all seems. Here's a good passage:
"For I have known them all already, known/them all--/have known the evenings, mornings, afternoons/I have measured out my life with coffee spoons."
This refers to how tedious and monotonous life is. One day is exactly like the previous, so it feels like he knows exactly what is going to happen. The coffee spoons reference is how we go through the exact routine every day (getting coffee in the morning, etc.). It feels like his entire life is spent living and doing the same things over and over.
Other references to daily life occur when he refers to how there is ample time to analyze and mull over life's meaning "before the taking of toast and tea," and how ridiculous it is that they go about speaking of silly, shallow things ("Michelangelo") at these tea parties, over and over again, when all he wants to do is address real issues, and talk about things that truly matter. Later, her refers to his days as "butt-ends," a negative description that shows how he feels his days are the useless butt-ends of living, worth only being spit out in disgust.
All of this refers to his weariness of the meaningless routine, and how he wants to get at the heart of matter and to have the courage to speak what he really feels. I hope that helped; good luck!