There are basically two types of searches a recruiter performs: retained and contingency. Under the circumstances you listed, I'm fairly certain this person is a contingency recruiter, which is also what I do.
A contingency recruiter fills a search order with a company and begins looking for suitable candidates. He then packages those candidates' information and sends it to his client, the hiring company. After receiving feedback from the client (hopefully), the recruiter then helps facilitate initial and follow-up interviews with the candidates the client has deemed worthy to proceed.
If the client hires a candidate brought forward by the recruiter, the client pays the recruiter a fee, typically a set percentage of the new hire's first year salary. If a recruiter ever asks you to pay him something, run for the hills like you are being chased by a swarm of angry bees.
Good recruiters find candidates like you in many ways, and sometimes in often unexpected places, so being contacted cold is not unusual; however, I would definitely do some research on the recruitment firm to gauge its legitimacy. If I see too many buzz words on a website (i.e. life-cycle, synergy, blah blah blah), I tend to become skeptical. Our job is fairly straightforward: we find talented people and help companies hire them. The end. It shouldn't be more complicated than that.
Most good recruiters specialize, working on jobs in one particular industry or a subset of an industry. That's helpful, especially if they understand what would be expected in the job in which they are trying to place you. And if a recruiter isn't willing to spend some time on the phone with you and learn about your goals and aspirations, pretend the bees are after you again. If I can't help a potential candidate, I try to be upfront about it so as to not waste anybody's time.
I hope this helps, and good luck.