What is equity in poker?

Equity vs pot odds vs expected value

Equity is a share. Pot odds are a price. Expected value is what happens when you combine them with fold equity and future streets. Calling is +EV when your equity exceeds the pot odds, ignoring implied odds. Folding a draw that is getting the right price is a leak. Calling a draw that is not, because the hand is pretty, is the same leak in the other direction.

How the Labs estimate it

Exact equity on a Hold'em flop is computable by enumerating every remaining runout. With more cards (Omaha) or more opponents, enumeration gets large, so the Labs run a Monte-Carlo: deal the remaining cards thousands of times, count wins, splits and losses. Five thousand trials is close enough to make a decision. It is not close enough to brag about 0.1% edges.

Range equity, not hand equity

At the table you do not know their two cards. You know a range: the set of hands they play this way. Your equity is against that range, not against the one hand you fear. Beginners compute 'I lose to a set' and fold. Regulars compute 'they have a set 12% of the time and I still have 38% against the rest of the range' and call. The Poker Math and NLH tracks spend a lot of grades on that shift.