Tasteful things are elegant, appropriate, or aesthetically pleasing. You may prefer to hang a single, tasteful holiday wreath on your door — while your neighbor decorates with a somewhat less tasteful 12-foot inflatable Santa surrounded by hot pink reindeer.
If you've got good manners, your behavior is tasteful. Having an eye for clothing and decor that's lovely (rather than tacky, ugly or disturbing in some way) is tasteful too. This adjective started came into use in the 17th century. It originally meant "tasting good" but it evolved to mean "having good taste."