At the most basic level, a home mortgage refinance is simply a new loan with new terms used to pay off an existing loan. Like any mortgage loan, various fees accompany the service of a home mortgage refinance whether the new loan is carried out by the existing lender or not. So then, if you already have a mortgage, why would you go through the hassle and pay a whole new set of fees to enter into a new loan?
You can get a lower interest rate that will reduce you monthly payment and often the overall cost of your loan. Similarly, if you have an adjustable rate mortgage (ARM) that is set to readjust in the future, now might be a good time to lock in what are - still historically - very low rates.
You can reduce or increase the term of you loan depending on your current financial situation. Also, if you are short on cash you can draw upon the equity in your home to take cash out.