I would nitpick this a bit: it's the proportion of the pot you own assuming no more betting. For example, imagine you get to the river with a bluffcatcher and your opponent bets pot. You know he's bluffing sometimes, but not enough for you to profitably call, let's say it's 20%. So your hand has 20% equity. But you have to fold to the bet, so the 'proportion of the pot that you own' is 0.

Steve,

If villian bluffs 20% and we have 20% equity doesn't that mean we should call

If villain bluffs 20% of the time, then we have 20% equity (80% of the time he has a value hand we lose to. It's the river so our equity with a bluffcatcher = how often he is bluffing.) Our pot odds are 2:1, so we would need 33% equity to call.

You only have pot odds of 33% if he is utilizing a pot sized bet. I don't see anything anywhere about specifically stating the size of the bet.

tbeckett if you were on the river with a bluff catcher and had precisely 20% equity and the bet sizing used by villain was such that your pot odds were 20%, then because your equity is equal to or greater than the pot odds you could call. This assumes your equity would not decrease due to rake or blocker effects. In this instance because pot odds = equity, the EV of such a call would be exactly 0.0000.

The sizing utilized by villain assuming he was only making a bet for you to have 20% pot odds would be a 33% bet size. (0.3333/(1.0000 + 0.3333 + 0.3333)). In this example, because your calls are effectively 0 EV (equity = exactly pot odds), then the frequency you should call would be calculated by making IP have his bluffs be 0 EV bets. This is done by calculating the frequency he needs you to fold when utilizing his bet size. In this example we've calculated his bet size as equal to 0.333 of the pot to give you 20% pot odds. This means when he bets 0.3333 he needs you to fold equal to or greater than (0.3333/(1.0000+0.3333)) = 25% of the time for him to auto profit with any bluff ignoring rake and blocker effects. As such, you would call with your bluff catchers 75% of the time.

To answer the original question, though. Steve is correct and his definition is good. Your equity is your share of the pot with your hand or range against a specific hand or range at any node in the game tree under the assumption that the rest of the hand is checked to showdown. As I said in one of the previous posts; you have equity, but you don't necessarily realize it all because there is betting going on in future nodes. Your equity is your pot share assuming you checked it all the way down. Your equity realization, is your EV/pot share divided by that value. It's basically stating what percentage of your equity do you actually get to realize in aggregate over all future nodes.

For example, imagine you get to the river with a bluffcatcher and your opponent bets pot

Probably could have made it more clear but I did specify the betsize