Anime is a word used by people living outside of Japan to describe cartoons or animations produced in Japan. Using the word in English conversation is essentially the same as describing something as a Japanese cartoon series or an animated film or show from Japan.
The word itself is simply the Japanese word for cartoon or animation, and is used by people in Japan to describe all cartoons, regardless of their country of origin. For example, a Japanese person would think that Sailor Moon and Disney's Frozen are both anime, not two different things from separate genres.
The correct Japanese pronunciation of anime is a-ni-me, where the "a" sounds like the "a" in art (but slightly shorter), ni sounds like the ni in Nick, and me is pronounced like the "me" in met.
However, the way anime is pronounced by native English speakers is slightly different: the "a" sounds like the "a" in ant, the "ni" sounds like the "ni" in Nick (the same as in Japanese), and the "me" is pronounced like the month of May.