The difference is that あります (arimasu) is the affirmative form of the verb and ありません (arimasen) is the negative. For example: えんぴつがあります。 enpitsu ga arimasu. (I have a pencil) えんぴつがありません。 enpitsu ga arimasen. (I don't have a pencil) I think this should be clear, but if you have any questions, please ask.

Essentially one is positive and one is negative. If someone asked you if you had something and you replied with Arimasu, then you'd be telling them you have it, and if you used Arimasen, then it'd be telling them you don't have it.