Strictly, 'anime' is just animations produced within Japan, but their distinctive style is sometimes how they are defined.
For example, Avatar:The Last Airbender is produced in America, but takes on a lot of the distinctive characteristics of anime:
Conversely, Panty & Stocking looks a lot like some western animation and is produced in Japan.
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: What differentiates anime from regular cartoons?