Goals are things that you particularly want your customers to do on your website. For example if you have an online shop, one goal might be for a customer to buy something, and other might be for a customer to sign up for your newsletter. By setting up goals in Analytics you can track these evens, see how many you're getting, where you're getting them from and how they get there - so you can optimise your marketing to focus on the sorts of customers that do convert.
another name for 'goal' is conversion. how many people are fulfilling your objective on the site, is your goal indicator.