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1.
The ability two or more close friends have when they've been friends for a LONG time. They tend to know what the other(s) are thinking, finish each other's sentences and communicate using almost no words.

More common in female best friend relationships but not limited to them, inside jokes could be one of the reasons why best friend telepathy occurs.
BFF 1: Wow, our best friend telepathy is getting ridiculous
BFF 2: I know! I didn't even have to say more than two words and you already knew what I was talking about!