That's a speciality of the Hungarian language. Both mean "I want" when translated, but there's a difference:
Akarok is the so-called indefinite conjugation. It is used whenever the verb doesn't have a direct object (something that has the -t suffix) or if the direct object is not a definite one, like in "I see a house" or "I hear some students". ("Látok egy házat" or "Néhány diákot hallok.")
Akarom is the definite conjugation. It is always used when the direct object is a definite one, which in most cases is designated by it having the definite article a (the). Like in "I use the car" or "I love that girl." ("Én csinálom az autót" or "Azt a lányt szeretem.") Azt, ezt, őt and a few other objects are also definite objects.
You'll learn more about the definite conjugation later on. :)
Megy (which is the dictionary form of menni) is pretty clearly a general "to go". The "walk" hover hint just comes up because there are a few instances which sound awkward when translated to English as "go". For instance "Mi megyünk itt" - "We're walking here."
"To walk", the specific movement, is better translated with sétál.
Why is the translation of No I want to go not acceptable? And how would a native Magyar translate No I want to go? It might be a difficult translation for me being an native Dutch and Dutch is known for being a blunt and direct language. Probably why I like Hungarian(s) better :-)
Punctuation plays a very important role in many languages. :)
- Nem akarok menni. - I don't want to go.
- Nem, akarok menni. - No, I want to go.
If there's no comma between nem and the verb, the verb itself gets negated, so the action does not happen. If there's a comma, the words don't influence each other.