Home equity is your share of the property, measured in money. The CFPB puts it as the value of your home minus the amount you owe on your mortgage, and any other loan secured on the home comes off too. A house worth £320,000 with £240,000 left on the mortgage holds £80,000 of equity, a quarter of its value.
It grows in two ways. Each payment's principal portion converts debt into equity, slowly at first because early payments are mostly interest. And the home's price moves: a 5% rise on £320,000 adds £16,000 without you paying anything, while a fall takes it away. If prices drop far enough that you owe more than the home is worth, the equity is negative and selling would not clear the loan.
Equity on paper is not what you would walk away with. Selling costs money: on that £320,000 house, agent and legal fees at 2% would take £6,400, leaving £73,600 in your pocket. That is the figure to use when comparing owning with renting, or when planning to use the proceeds for the next deposit.
Equity is the mirror image of the loan-to-value ratio: at 75% LTV you hold 25% equity. Lenders use it the same way, so more equity usually means a cheaper rate when you remortgage. You can also borrow against it, through a further advance from your lender in Britain or a home equity line of credit in the United States, but that turns equity back into debt.
The rent vs buy calculator counts the buyer's equity after selling costs at the end of the period you choose, and sets it against everything the buyer paid out, so the comparison with renting rests on cash you could actually take away.