The Word Anime
If you do a search on 'what is anime' or 'anime introduction' using a web search engine, you'll find tons of links and descriptions. What I am going to do here is to sum them up. So, what is anime? Anime is the most common word used by fans to refer to Japanese Animation.
Is anime the same as cartoon? Technically yes, however for anime fans, anime is not cartoon. See the definition above, anime refers to Japanese animation. So, the rule of thumb is as simple as: if it's not originated from Japan then it's not an anime (while the contrary is not true).
People usually think that anime is the animated version of japanese comic (manga). While in most cases this is true, however, not all anime is based on manga. For example, some anime are based on video games like Sakura Taisen and Tales of Eternia.