If Antonio cannot pay back Shylock, Shylock demands that Antonio forfeit a pound of his flesh. The deal makes its first appearance in Act 1, Scene 3.
Go with me to a notary, seal me there
Your single bond; and, in a merry sport,
If you repay me not on such a day,
In such a place, such sum or sums as are
Express'd in the condition, let the forfeit
Be nominated for an equal pound
Of your fair flesh, to be cut off and taken
In what part of your body pleaseth me.
I remember reading that quote for the very first time, and I thought the pound of flesh was some hidden metaphor or Shakespeare thing. I didn't realize that Shylock literally wanted to cut off a pound of Antonio's flesh. That's just gross.
The reason Shylock makes such a deal is because he hates Antonio. He hates Antonio because Antonio is a Christian. Shylock hates Antonio, because Antonio undercuts his business by giving out loans with no interest. Antonio has also publicly insulted Shylock and spit in his face. The demanded pound of flesh is a legal way for Shylock to seek revenge and inflict physical pain upon Antonio.