Hi Limbogirl. I'll offer my $.02 and hopefully something will click:
The "higher self" is a new age idea that has its roots in Eastern religious tradition, which typically involves the idea that humans are reincarnated repeatedly until we "get it right". At that point, you achieve Nirvana, which is comparable to heaven, but is described as more of a place of perfect and eternal peace and interconnectedness with the universe. The higher self is basically your eternal soul or the "real you", which always has existed and will never die. That soul is incarnated in human form as part of its journey and search for Nirvana.
I'm sure that I'll get corrected on what I've said, as I personally subscribe to the Western tradition of heaven, hell and only one shot at this life, but hopefully this will help.
Also, I found this Wikipedia article
that may clarify things.