Now, I'm sorry to disappoint you all but this is false. However, cutting off split ends will prevent them from splitting up the hair shaft even more, and this does enable the hair to grow healthily. So there is some essence of truth in it afterall.
When your hair starts to split at the ends, it keeps splitting up the hair shaft. This can prevent the hair from getting any longer, because the amount that it grows is also the amount that splits and snaps off at the ends. (This can have many causes mainly heat and chemical over-exposure and damage.)
Healthy hair shaft
Therefor it is a good idea to keep getting your trim every 6 to 8 weeks. The time period between visits can differ per person as some people's hair growth is faster and therefor need their hair cut monthly to keep it in shape.
I hope this has been informative ;)