This happens on a few other sites as well.
Clearly, I'd like the form to be empty when I start a new question! I'm using the newest FF browser.
Stack Exchange sites will save a question or answer you're composing after a while. You'll see a "draft saved" message when this happens. (If you switch to another browser, log in, and go to the same page you'll see the stuff you entered will re-appear, confirming it's actually saved on the server.) Sometimes this is helpful, but sometimes it's annoying, because there's no way to discard the saved draft.
To report issues like this that happen on all Stack Exchange sites, your best bet is to post on meta.stackoverflow.com. However, a "discard draft" feature has already been requested there but declined: Manually reseting+discarding saved question drafts. --- Update: Another request is here: Add a clear button when a saved draft is loaded
The "save draft" feature was originally requested and implemented as described here: Allow questions to be saved as drafts prior to posting. According to that page, only one question or answer draft is saved at a time, for up to a week. If you start a new post, the previous draft is discarded.
As a work around, you can enter the following into the address box to discard the draft saved on the Ask Question page of the current Stack Exchange site you're on.
To make it easier to use, you can save it as a bookmark. Call it something like Discard Draft. Then if you notice a draft question has re-appeared, you can just click on the Discard Draft bookmark.
The StackExchange sites will save unsubmitted forms in your cache so that you can return and finish a question later if you didn't finish it and submit it. Usually, once you click the button to submit your question or comment that gets cleared out. Clearing your browser cache should be sufficient if you find it isn't getting cleared, unless you have some sort of form auto-completion enabled that is storing the data.