With a fixed-rate mortgage, your interest rate stays the same, or "fixed," throughout the term of the loan. Therefore, your mortgage payment stays predictably the same, making it easier to plan your spending each month. However, lenders typically charge a higher interest rate (to make up for the lost income that could be gained from a rate increase), which lowers the total amount you can borrow. And though you're protected from rising interest rates, you're also stuck with a certain rate even if the going rates fall.
The most common fixed-rate mortgages are 15-year and 30-year, which refer to the time you have to pay off the loans. The interest rate on a 15-year mortgage is usually lower than a 30-year mortgage, meaning you'll pay less over the life of the loan, but you can expect your monthly payments to be higher since you have half the time to pay it off.