I was working on create a Word macro in Microsoft VBA, and somehow it ended up creating a lot of these projects. They look empty, but I can't remove them. These documents don't exist, at least that I can see, and I think they were created while I was debugging the original macro.
As discussed in the comments, you had multiple instances of Word running, with one document (i.e. "Project") open in each, as revealed by looking at Windows Task Manager.