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.
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.