All investors have pet theories. They may call these theories "theses" or "themes," but they boil down to the same thing - closely grouped sets of ideas which the investors want to be true. Investors will usually fund companies that seem to stand a chance of making these ideas real. At YC, we have quite a lot of pet theories, which end up getting expressed through our RFS.
Knowing the pet theories of the investors with whom you're talking is helpful. They may be more likely to fund startups that fit into pet theories and are likely to know a lot more about those theories than they do about other fields. That's great if you know what you're doing, but dangerous if you're half-assedly working on something. Let's assume you're in the first camp, because the second group shouldn't be talking to investors anyway.
You can learn a lot about the pet theories of investors by reading what they've written or spoken about in the past. Some investors - Fred Wilson, Andy Weissman, Chris Dixon - make this easy by writing blog posts that frequently reference what they think about and why they make the investments that they do. Other investors work at firms dedicated exclusively to particular pet theories. You can learn still more looking at an investor's career and past investments. These are all pieces of information that can teach you about how an investor thinks, which will allow you to prepare better for actually meeting them.
Knowing an investors' pet theories can also help you get a meeting. An email directly referencing something near and dear to an investor's heart will get a response much more easily than something generic. At the same time, the hurdle for getting a meeting on a pet theory is going to be high because the investor has likely seen many teams and ideas in the space.
The really cool thing about meeting with someone who has a pet theory about what you're working on is that you won't really pitch them, you'll have a real conversation focused on the heart of what you're doing. These investors will be unlikely to ask simple, surface level questions. You'll be engaged and thinking the whole time, which should lead to better answers, and the best demonstration of how good you are.
Things will start to get really interesting when you begin to challenge the preconceived notions that an investor has as a result of how much he's thought about a given problem. Chances are that if you're doing something new, this is going to happen. It's where you'll be able to evaluate the quality of the investor. The best of them are flexible. They'll adapt their frameworks in response to new information and knowledge. The worst will be dismissive of ideas they hadn't considered before.
There are also plenty of situations in which someone hasn't thought that deeply about a theory they discuss at length. Maybe they want to sound smart or look cool. Regardless, you should be able to figure that out pretty quickly and move on.
You should learn about an investor's pet theories when deciding if you should talk to them, and when preparing to actually meet. In the end, this is just one of the pieces of information you should have. It isn't as important as building a great business, but understanding the picture will help you pitch better, so spend some time on it.
 Keep in mind, though, that investors generally don't only invest in their pet theories.
 This seems so basic, yet I get enough generic emails that I'm convinced it has yet to sink in.
 As always, warm intros are an even better bet.
 True in all situations, not just those related to pet theories.