A product can be deemed non-kosher due to the presence of an "unclean" animal or an animal that was not properly slaughtered. Most commonly, when people discuss non kosher animals, they immediately think pigs. Yes, according to Jewish beliefs, pigs are off limits. The guidelines say that "anything which chews the cud and has a cloven hoof is ritually clean, but animals that only chew the cud or only have cloven hooves are not" (Leviticus 11:3-4) Confusing, I know. Make is easier on yourself here. Rabbit and pig are probably the only two animals you will come across in your daily life....unless camel is something you snack on.... Also know that anything that "crawls the earth" is unclean (no spiders) and birds of prey, including the fish eating ones, are a no no. Fish are also totally fair game.
Usually when Kosher foods are spoken of, people are referring to the slaughter of that animal. Jewish Dietary Law dictates the exact fashion in which an animal should be killed. Most importantly, you CANNOT eat an animal that has died of natural causes. Also, before and after slaughter, each aspect of the animal is inspected for good health, including the organs. This stems from the thought that the animal had something wrong going on inside, so therefore, it is unclean for you to ingest those diseases. This is a long, very detailed process. I highly recommend you look over this article and read about the in's and out's to inform yourself a bit further:
http://en.wikipedia.org/wiki/Shechita
For your reference, these are some common labels used on Kosher food packaging
Now, with all that said, this is a great place for new veggies to start. Obviously, at this point your are still eating meat. Much like the organic label, you should be skeptical about what you are actually buying. Organic products endorsed by the USDA only are questionable. Keep in mind that those rules are really suggestions and the organization itself is run by the people that produce the products. They WILL have their own best interest in mind. Kosher foods should be viewed with a chip on your shoulder as well. Many of these supervising rabbis are not on the property 100% of the time, are being paid by a meat processor to do their job and maximize profits, and also do not witness the entire slaughter and health of the animal each and every time. Like I said, this is a great way to start eating responsibly, but seriously question where you get your products from!
Shalom :)
<3 J