Intuition is applied more to humans. It means some instinctive knowledge or belief that we feel without having to have immediate proof of it - we don't have to see it. I emphasize that this applies to more rational thought. "My intuition tells me that the stock market is due for a fall." "Her intuition told her that he was lying." Instinct is used for some biological feeling, both in animals and humans. It is usually considered more basic than intuition. Fear is an instinctive response. We feel it physically as well as mentally. I can say that geese have an instinct to migrate with the seasons. I would not use 'intuition' to describe that. "His intuition told him that the tiger was in the area, close to him." "Cats have an instinct to defend their hunting territory."

well explained by fdmaxey, but if you want a shorter version here it is. Intuition: make your think less before action Instinct: action/reaction without thinking