"I do not have it."
ありません means that "it" doesn't exist.
もっていません means that you don't have "it" with you at the moment.
Just so no-one gets confused like I did because of their similarity: 持って（もって）and 待って（まって）have different meanings. Motte means ‘have’ and matte means ‘wait’.
Yeah, but since many learners watch anime, matte is probably the first word they learn in Japanese. Ahahaha.
持つ means hold as well as have - if you like you can think of it as I'm holding/carrying it, which is a way of saying you have something in your possession
But really this is just how you express the idea of having something in Japanese
That would be まっています, but this sentence has ません, which makes this sentence mean the opposite.