That isn’t an icon but a windows Vista or Win7 gadget (depending on your OS) and allows access to some of the avast functions, you should also be able to reduce the size.

If what craigb suggests doesn’t work, e.g. it reappears after you reboot, then you will have to take another step.
Avast Gadget removal - Control panel → Programs and Features → avast! → Change → uncheck the box “avast! gadget” click Next and OK your way out.