"Look who's talking" is a present-day analog of the old Latin "Tu quoque" (You too), which has other modern evolutions in present-day Romance languages ("Y tu", "et vous") which figuratively mean the same thing. It is an inductive reasoning element used to cast doubt on one's opponent in an argument or debate; The context is that the opponent is advocating that either the speaker or a third person should exude some moral quality which they do not themselves possess. The term thus implies that the other person doesn't do what they are advocating, so why should anyone else?
Dad - "Son, I'm sick and tired of you coming home at midnight smelling of booze. You should drink less and come home earlier."
Mom (to Dad) - "Look who's talking! You only got here thirty minutes before him, and I smelled whisky on your breath!"
Popular synonymous adages include:
- Listen to the pot calling the kettle black
- Take a page from your own book
- Practice what you preach
- Holy Bible, Matthew 7 (NIV): "Why do you look at the speck of sawdust in your brother’s eye and pay no attention to the plank in your own eye?"