Mind figures things out.
Intuition knows things spontaneously.
Mind only operates on previous knowledge
Intuition has access to all knowledge, past, present and future
Our mind has to go through an elaborate rational process when it works to figure things out. Our intuition knows things directly with absolute certainty without going through an elaborate mental process.
An analogy is called for here:
In Algebra, you have to work the formula to figure out the answer to a mathematical problem whereas your intuition has the ability to spontaneously know the answer to the problem without working the formula.
Our educational system teaches us how to use our mind but does not teach us how to use our intuition and because of this people struggle solving problems in their life when struggle is not neccesary at all.
Recommended Book to help you develop your intuition:
FutureSight By Barry Kaufman
Read an excerpt from this book at Amazon.com by Clicking Here