I admit I can't find the exact post, but I remember seeing something online that was something along the lines of "Transgender people don't change their gender. They might change their body, appearance, and name, but that's only to match the gender they've always had". And I think it's a pretty good explanation of the entire concept of being transgender.
I think it's also important to remember that sex and gender are not the same thing. Sex is biological. Is Caitlyn Jenner still of the male sex? Yes, I suppose so. I don't know if she's started taking hormones or had surgery done, and, if those are the case, then the lines defining what sex she is could be blurred, I suppose, but, if we're speaking purely in terms of genetics, then, yes, she would still be of the male sex (which I'm assuming is what you were referring to with the "isn't he still a guy?" comment), but, sex isn't gender, which makes it a bit of a moot point.
Gender is psychological. It refers to whether or not you identify as being male or female, and is therefore a much more complicated topic than sex. I won't hash out all the particulars here, but, in short, that's what the difference is -- sex is body, gender is mind.
People who are transgender essentially feel like their body doesn't match their gender, and often feel like their body is foreign or wrong to them, which is why they may choose to have surgery done to change these aspects of themselves, and why they might change their name, etc.
Think of it this way: if you were a man, would you feel comfortable having boobs and a vagina, having a feminine name, society telling you to wear feminine clothes, and hearing everyone refer to you as "she"? Probably not. Well, a trans man would feel the same. That's why he would probably want to change his name/pronouns, as well as the clothes he wears or perhaps even his body's own sex organs. (Though not every trans person goes through surgery or follows the exact same set of steps to transition, I might add. Everyone's different, after all. Regardless, it's not their body that matters -- it's the state of mind.)
As for whether or not Caitlyn Jenner deserves to be the 'Woman of the Year', well, that's a whole other debate, even if you fully and unquestionably accept her as being a woman. I'm not going to act like I know enough about any other potential candidates to say whether or not she deserves that award.
But I will say this: even though she's not exactly unique in being a trans woman, she is somewhat unique in the fact that she's stirred up a lot of attention and recognition for trans people. She's brought the topic more into the forefront and made more people aware of the concept of being transgender. Yeah, not everyone accepts her and some people still vehemently deny that she's a woman, but, a lot of other people have accepted her, and the fact that Caitlyn Jenner is practically a household name now is making the whole transgender thing a lot more normalized -- something that isn't just some weird thing that people would feel the need to hide in fear of other people not accepting them or even thinking that they need to be "fixed" somehow.
I can't speak for everyone, but I've heard a lot of trans people say that Caitlyn is sort of inspiring in the regard that she represents a certain level of hope for them in regards to the direction that things are going. Caitlyn isn't the only trans woman, no, but she's certainly gained a lot more attention and recognition than most trans women do, and her coming out has done a lot for the trans community in the form of raising more awareness and acceptance. The whole thing has stirred up a lot of anger and controversy, sure, but I suppose it's better that society is actually talking about these things and giving trans people more of a chance to come out and be supported than just treating trans people like some sort of taboo topic and making them feel like outcasts or mistakes.
And I'm assuming that that is the reason why she was given that award. Whether or not you agree is a different topic, but, I can definitely understand the rationale behind it.
Help that clears things up for you, OP.