computer attack?

Strictly, it means your computer was really busy with something at the moment you were typing. There's no way to know simply from that fact what was going on, and whether or not it was harmful.

Chances are it's nothing at all, but if you're really concerned, you can do the usual paranoia checks: disconnect from the Internet, scan for viruses and other malware, check running processes for foreign objects, double-check your security settings, and change any passwords on your local machine.

IE does this on certain machines. I'm not sure why (it did this on all the machines we had when I was at school, and sometimes on one of the work machines, for example).

It could be as simple as IE's history being huge and it's trying to complete as you're typing. To be safe, get spyware and antivirus stuff installed. You can never be too safe, and you're running IE, so that's just asking for trouble. You should consider switching to Opera or Firefox instead. Besides being safer, their developers actually implement those "feature" things, and you know, didn't drop development in 1998. Nor do they leave critical vulns open for years before they get around to fixing them..