Strictly speaking, 'anime' is just animations produced within Japan, as it's the Japanese word for cartoons/animations, but their distinctive style sometimes dictates how people define them term 'anime'.

For example, Avatar:The Last Airbender is produced in America, but takes on a lot of the distinctive characteristics of anime:
![enter image description here][1]

Conversely, Panty & Stocking looks a lot like some western animation and is produced in Japan.
![enter image description here][2]

The definition of anime is a topic that is frequently debated, so there seems to be no finalized answer. It's probably best to describe shows outside Japan as 'anime-styled' rather than as 'anime'.

Also, this question might be of interest: http://anime.stackexchange.com/questions/69/what-differentiates-anime-from-regular-cartoons

  [1]: https://i.sstatic.net/lZjjf.jpg
  [2]: https://i.sstatic.net/yOsdC.jpg