Equity is the difference between the value of the home and what you have left owing on your mortgages (liens or any other debt secured using the property). Until you sell the building, it's all pretend money. You can borrow against equity (with equity-access loans), but it's very expensive debt, particularly if the value of your home drops when you need to sell it. You can end up walking away with a lot of debt, and no home.
Which is what happened to millions of people with the last housing bubble burst.
It can affect your credit score, and end up costing you a lot of difference in mortgage rates if you need to rewrite a mortgage when the property value is low (the more debt is tied up, the 'higher ratio' your house in worth-to-debt... and high ratio morgages--less than 25% equity--do not get as good an interest rate as low-ratio--more than 25% equity--mortgages). A few % can mean paying thousands more $$ for the house.
at 11:50 AM on Jan. 25, 2010