Home equity
Home equity is the share of your home's value that you own outright: the home's fair market value minus what you still owe on the mortgage.
New Jersey example
Say a made-up Ocean County home would sell for $500,000 and $320,000 is still owed on the mortgage. The owner has $180,000 in equity. Paying down the loan builds equity, and a rise or drop in the home's value moves it up or down too.
Official source
This is a plain-English summary. Rules and dollar amounts change, so check the official source or a professional before you file or sign anything.