Aesthetic design is all about getting the look right. If you are good at this it means you will be able to design sites that not only look good but are appropriately designed. Different designs convey different messages to an end user, so it's essential that a design matches the site's message.
Out of the three components of web design, aesthetic design is surely the one that people most identify as being design. One thing I find interesting about aesthetic design is that it is deceptively difficult. I remember once designing a poster and showing it to a friend who commented "oh it's just a few lines and some text, you must have done this in about ten minutes" - ah the joys of being a designer!