What do accents do?
How do they change the word/ letter? Do the particular accents make a difference because as long as I put one in the work they seem to accept it, even if it the wrong one?
Are they truly important?
Getting the accents wrong on a word is the same as spelling it incorrectly. Duolingo lets us skate by with a warning to make the lessons a bit easier, but you still have to learn accents if you want to be able to write well in French. How they change pronunciation depends on which accent and which letter you're talking about. For instance, a cedilla (ç) turns c into an s sound in situations where you'd otherwise have to say a k sound, and an acute accent (é) turns a silent e on the end of a word into the sound ay.
As anomalocaris has already pointed out, accents can change the pronunciation of a word. Garçon is probably a good example of this.
There are other words where the accent alone completely changes the meaning or usage, but not the sound. Although you could probably work it out from the context, it is still a useful aid to comprehension, just like using capital letters and full stops. For example: a (has) / à (to), la (the) / là (there), tache (a mark, spot or blotch) / tâche (a task or job), des (some) / dès (from, since).
And finally, one where pronunciation and meaning change: cote (quotation) / côte (rib) / côté (side).