It is the avast update process and as such is protected by the avast self-defence module.
You say "It keeps running and not finishing." It should close when it has completed, I don't see it in my task manager, so it could be something on the system could be blocking it (firewall perhaps ?).
What do you mean by this, e.g. are you getting any error messages, if so what ?
Have you only recently installed avast ?
What avast program, version and build number are you using ?