What is the difference between mange and manges?
There are different conjugations. If you take a verb, you can conjugate it in a few ways... In English, we say "I eat, you eat, he eats, we eat" etc. In French you would conjugate the verb MANGER: Je mange, tu manages, il/elle/on mange, nous mangeons, vous mangez, ils/elles magent. Notice the different ending for the different conjugations. Mange would be the conjugation for il/elle/on/je (he, she, we singular, I) and manges is the conjgation for tu (you singular).
I recommend learning about verb conjugations on About.com – http://french.about.com/od/grammar/a/Introduction-To-French-Verbs.htm
As a beginner, you probably only need to worry about the present tense conjugations of être, avoir, and the regular verbs (-er, -ir, and -re).