A lot of people are always asking "what is Kosher?" The truth is, it's the same thing. When all of the ingredients inside a food are "kosher", the food is then labeled as "kosher." One non-kosher ingredient can make the entire food not-kosher.
There are several factors that determine if an ingredient is NOT kosher:
Because of how easy it is for anyone to just claim a food (or ingredient) is kosher, many people don't eat kosher foods that are not certified by a Kosher Supervision. Kosher Supervisions, such as "RCC" and "O.K" require an orthodox Jew (who is well versed in the laws of kosher) to supervise the facility making the ingredient/food to ensure all food is in fact kosher.
One final (and big) difference about kosher, is that meat and dairy products are not allowed to be mixed (or eaten) together. Therefore, kosher meat restaurants are not allowed to use real cheese for their burgers, and typically go with a soy alternative.