Recently, while looking through my websites files, I found some weird HTML file in a random directory named "files". The HTML page was about drawing polygons or something. I quickly deleted it and just moved on with what I was doing... Should I be worried about how this file showed up randomly on my websites files, or is this a normal thing.
Your question is somewhat vague. Can you offer any more details?
What was it, what was in it, where was it, and what webapps do you have installed?
Also, check your FTP logs to see if anybody has accessed the site by FTP who shouldn't have.
There is only one FTP created and it is the one run from my home computer. It appeared in an otherwise empty directory called "files" on the main public_html directory. The file was called "An introduction to wavelets and haar transform by Musawir Ali" When I opened the file it was what it said it was. The only thing I had installed at that time was a microblog software called Page Cookery...
And you're sure it hasn't been accessed from a different IP? I only had one FTP account for my site, but that didn't stop a hacker using it to upload a file.
If you're sure that the directory or the file didn't used to be there, then I'd say you have a problem. If you think you might just not have noticed it, then who knows? A search for that title leads to the University of Central Florida site. Maybe somebody decided to save a copy of the page?