In my belief system Intuition is a combination of a couple of things.
First it is the remembered experiences of past lives. Although few of us are able to remember our past completely during our current incarnation our true self (our higher self, our soul) retains those memories and provides insights to us because of them.
Secondly we have ancestors and spirits that watch us, most of us are unable to hear or see them on a continuous basis, however our true self is able to communicate with them and they sometimes offer us insights to keep us from harm and trouble.
Lastly, the deities that you worship (give honor to) will from time to time give instruction to your true self on what you should do in a given situation. All three of these things come through to us as intuition. Some of us are more intuitive than others, this is because the more intuitive people have learned to trust there true selves and act on the intuitive messages they are given. The more a person relies on and uses the intuitive messages that they are given the more they receive those messages.