Difference between arimasen and wakarimasen?

"wakarimasen" (分かりません) is the polite negative form of "wakaru" (分かる, "to understand"), so it would mean "do not understand".

So, for example:
私は英語が分かりません。 / watashi wa eigo ga wakarimasen. / I don't understand English.

"arimasen" (ありません) is the polite negative form of "aru" (ある). ある is a verb that expresses the meaning of "to be" or "to exist" (for inanimate things, like objects). It can also take on a few other different meanings depending on context.

Example:
ペンがありますか？ / pen ga arimasu ka? / Is there a pen? (lit. "does pen exist?")
いいえ、ありません。 / iie, arimasen. / No, there isn't. (lit. "no, does not exist")

As you can see, don't take the meaning of arimasen to literally mean "to exist" or "to be" - it just expresses the idea of something being there.

arimasen is basically "not exist" ("not be" sometimes "not have")
wakarimasen is "not understand" "not know"

Edit. Arimasu is for inanimate objects (imasu for people, animals, etc)
Edit 2. if you want to learn more go here C:
http://www.learn-japanese-adventure.com/arimasu-imasu-existence.html

The letters W, A and K.