What's it mean to have abnormally long fingers?

Might be. Long fingers occur in Marfan's syndrome - are you tall, have some eyesight issues, have prominent chest bones, is it in the family. Of course with long fingers you have an advantage in playing some musical instruments so it is not all bad.

Related Questions

Are abnormally long fingers a medical concern?

Perhaps. Isolated long fingers are usually of no concern. There is a condition called arachnodactyly which can be associated with other conditions - i.e. Marfans, etc. If you are concerned, might I suggest a consultation with a pediatrician, plastic surgeon or geneticist.