The ultimate goal of a mortgage is to repay the debt and therefore own the home free and clear. At the beginning of a mortgage term, most of the monthly payment goes to paying the interest. Eventually, more of the monthly payment goes to paying the principal. These two pieces of the payment combine to repay the debt. This process is known as amortization.
Amortization is the process of gradually owing less debt because of regular payments of interest and principal. The amount of the monthly payment is calculated so that it is large enough to pay off the debt at the end of the term of the loan.
Fixed rate mortgages are fully amortizing. For example, if you have a 30 year fixed rate mortgage, at the end of the thirty years, the loan is paid off in full. If you have a 15 year fixed rate mortgage, the loan is fully paid off in fifteen years. That is why the monthly payments for a fifteen year loan are more than for a thirty year mortgage - you have to pay off the loan twice as fast. Of course, you also pay less interest for the life of the loan with a shorter-term mortgage.
Adjustable Rate Mortgages, or ARMs, also are fully amortizing. An ARM has a lower initial interest rate than a fixed mortgage. However, it only keeps this initial rate for a relatively short amount of time depending on what type of ARM you have. Once that period is over, the interest rate of an ARM then goes up or down usually every year over the term of the loan. Even though an ARM has a varying interest rate, it still amortizes, usually after 30 years.
Because of amortization, if you keep your mortgage for the entire loan period, at the end of that time you will own your home free and clear, unless, of course, you have taken out a home equity loan or second mortgage.