Like Ashraf explained, "möchten" means "would like" and "wollen" means "to want". We prefer to say "ich möchte" because it sounds more polite while "ich will" often sounds like "I demand". For example, if you are in a café, the waiter will ask you: "Was darf es sein?" (which means in a transferred sense: "What may I do for you?") The correct answer is: "(Ich möchte) einen Kaffee/Tee/Kuchen bitte." ("I would like to have a coffee/tee/slice of cake, please." You'll never want to say: "Ich will einen Kaffee/Tee/Kuchen." ("I want/demand ...") Many children (and childish old people) tend to say "Ich will ...".

"Möchten" (would like) is more polite than "wollen" (want) but "wollen" also expresses a stronger wish.