I don't mean to discourage, but it seems to me that profs say this to everyone and it rarely leads to a publication.
Well, if you're in a good grad program, the odds are that a lot of students are from time to time producing potentially publishable work. Especially for qualifying papers -- it is somewhat problematic if they aren't, in fact. So it shouldn't be that much of a surprise that many students hear this at one point, and I do think most professors who say this are indicating something about the work in particular, not the student.
But on the other hand the road to publication is difficult, both practically and psychologically. The main reason this kind of comment rarely leads to publication at this stage is because there's a lot of work, and typically also some major mental barriers, between "potentially publishable" and "publishable" for a young grad student. Most people won't really act on this kind of comment, because (I think) of the mental barriers. The professor doesn't mean by this "go submit it to Nature tomorrow". Rather, "if you spend months revising, and then more months dealing with reviewer comments, it is very likely to be published in a decent specialist journal." But this doesn't mean you shouldn't do it -- you have to start some time (the earlier, the better), and it might as well be with this paper.