What is the difference between mange and manges?
It doesn't seem to be explained in the lesson and I can't see the difference between when each one is being used.
Manger means to eat. I think mange is used for the "Je" and "Il/Elle" form while manges is used for the "tu" form.
They don't really ever explain it, but that's called "conjugating" a verb. Basically there are different versions of each verb, depending on things like the subject (I, you, they, he/she, as nbeckman said), and sometimes the tense (past, present, future). If you go to the vocabulary tab at the top you can find a list of all the conjugations for each verb they've taught you so far, though it would be nice if they had a lesson specifically on conjugation rules and stuff.
there are more than just two versions. when you hover over a word within the lesson, on the bottom of the pop up is a green button with the word conjugation. if you press it, it comes up with conjugation list for that word. hope this helps.
The verb is a different word depending on who is eating: Je mange/Tu manges/Frank mange. It's like English with "to eat." You would say "I eat" and "He eats," and while they're different words, they mean the same thing and would just be used in different contexts.