"Kosher" is a series of laws. But how do we know that a food product complies with these laws? So there are many companies that will go in and certify a food product as complying with the kosher laws. (They'll inspect the factory and ingredients, for example.) Here is a list of some of them.
So a circle-U means that the Union of Orthodox Jewish Congregations of America certified this product as kosher. The Star-K means it was certified by a group of rabbis headquartered in Baltimore. Each certifying organization (or individual) has its own symbol.
Some of these certifiers have different standards (often based on different rabbis' interpretations of the kosher laws), and thus some people prefer products with certain certifications. For example, just about any plain-old cow's milk in America could be certified by the OU or cRc, but the Star-K will only certify it if a Jew is regularly observing the milking.
In America there are the "big five" organizations: Star-K, OU, cRc, OK, Kof-K -- who account for a great deal of the kosher market. As one food ingredient goes into another food, they work together and compare standards.
A plain "K" on a product simply means "manufacturer says it's kosher." It could be "we have a reputable certifier checking this but we're not putting their symbol on it"; it could be "this is something so obviously kosher (e.g. plain water) that we don't feel like getting external certification"; or it could be they're using a more-controversial definition of the kosher laws.