Most people have covered the equity part, but not the "buying things with equity" part.

Equity is how much your home is valued at minus how much you still owe for it. Once you reach a certain amount of equity, or certain amount of house you own vs the bank owns, the bank is then willing to loan you money against that equity (Home Equity Line of Credit or HELOC). These types of loans tend to have a significantly lower interest rate than traditional loans. The other thing you can do is leverage the equity in your house towards a second mortgage on a seperate property. This let's you have a second rental property or similar, again, at often a lower interest rate.