Equity is the amount of the home that the buyer has actually paid for. It is made up of the down payment plus the amount of principal that has been paid.
A mortgage payment is made up of interest, which is the amount you are paying the lender to give you the loan, and principal, which is payment toward the cost of the house. The more equity you have in a home the more you actually own. At each mortgage payment you are paying a portion toward interest and equity so the amount of equity increases with each payment.
Equity is important if a homeowner needs to refinance and when the property is sold. The larger the portion of the property the borrower owns, the less he or she will need to pay for when refinancing. In a sale, the equity is the profit that the homeowner gets.