Something that's dressy is characterized by elegant, expensive, or fancy clothes. You look dressy when you wear a ball gown, high heels, and a tiara on your head.
A person can be dressy, and you can also describe the person's outfit as dressy — if it's a tuxedo with a bow tie and cummerbund — or an event as dressy, if it requires you to wear such an outfit. A dressy wedding calls for formal clothing, so you probably shouldn't wear a fisherman's sweater and sandals. Dressy was first used in the 18th century, from dress.