Picture your home in two parts. One part is yours. The other part is still owed to the bank.
The part that's yours is your equity.
On day one, your equity is your down payment. Every payment makes your part bigger. If home prices go up, your part grows too. If they go down, it shrinks.
Later, you can borrow against your equity, for example to fix up your home. Lenders usually let everything you owe on the home add up to 80% of its value at most. The refinance and HELOC calculator shows how much.