The "a" icon rotates whenever the avast! resident protection is scanning something (e.g. when you start an application). It's just an information for you that the resident protection is active, that's all :-)
Of course, avast! can be configured to download updates automatically (I think it's configured that way by default, at least for the virus definitions). If you go to the program Settings and select the page "Update", you can specify the updating options.