I think the wording is quite descriptive, the update package isn't working/broken.
Whilst a reboot may resolve this, if it doesn't try a repair of avast. Add Remove programs, select 'avast! Anti-Virus,' click the Change/Remove button and scroll down to Repair, click next and follow. You may need to reboot after the repair.
I assume that the system is not fully protected message relates to not being able to update the virus definitions (out of date). You need to open the avastUI (click on the avast icon) and expand the Summary section to see exactly what it reason is.