Firefox will do things like that. What it's actually doing, in the majority of cases, is turning into a zombie process. That is, it's running but not responding.

When this happens, almost always simply killing the process and restarting Firefox will solve the problem. If you try and start another instance of Firefox, either it won't start up, or in rare cases it will want you to set up a new profile. Even if you set up a new profile, your old data would still be there, just in a different location from where Firefox was looking for it.

Odds are, this won't happen again, however, you can back up your profile data if you want. Might be easiest if you use a program to do it, such as MozBackup. Then store that resulting backup file on a CD or some sort of removable media.

Finally, cache is the term given to the stored copies of pages you visit that the browser keeps. This is done to speed up repeated access to the same sites. If nothing has changed, then to save time and bandwidth, the browser just loads the copy from the cache. So clearing the cache would be deleting all of these files. Sometimes Internet Explorer gets hung up on corrupted files in the cache, but Firefox doesn't. Mostly because IE allows for executable content to be embedded into web pages, Firefox will ignore it since it's a security risk. The only thing it will really affect is your free disk space to a small degree.