A mortgage is a way to use one's real property, like land, a house, or a building, as a guarantee for a loan to get money. Many people do this to buy the home they use for mortgage: the loan provides them the money to buy the house and the loan is guaranteed by the house.

In a mortgage, there is a debtor and a creditor. The debtor is the owner of the property, while the creditor is the owner of the loan. When the mortgage transaction is made, the debtor gets the money with the loan, and promises to pay the loan. The creditor will receive money back with interest over time (usually in payments made each month by the debtor). If the debtor does not pay the loan, the creditor may take the mortgaged property in place of the loan. This is called foreclosure.

Below is a chart of various types and uses of mortgages!

30-year fixed-rate - Long-term mortgage designed to be paid off in 30 years at a set interest rate. 
Used for: Home purchase, mortgage refinance, cash-out refinance, home equity loan, jumbo mortgage, FHA, VA, USDA
15-20 year fixed-rate - Medium-term mortgages designed to be paid off in 15-20 years at a set rate
Used for: Home purchase, mortgage refinance, cash-out refinance, home equity loan, jumbo mortgage, FHA, VA.
ARM - Mortgage with interest rate that varies over time, based on market conditions.
Used for: Home purchase, mortgage refinance, home equity loans, HELOCs, interest-only loans, jumbo mortgages.
Interest-only - Interest payments only for a fixed period of time before principle must be paid off.
Used for: Home construction loans, HELOCs, jumbo loans, ARMs, balloon payments.

Piggyback Loan  
A second mortgage, or lien, used to cover part of the purchase price of a home
Used for: Partial or entire down payment in order to avoid paying for mortgage insurance; funding jumbo portion of high-end home purchase so that the rest can be covered   with a lower-rate conforming loan. Fixed-rate, ARMs, jumbo loans.
Home Equity Loan
Loan secured by the equity in the borrower's home; that is, the home serves as collateral for the loan. A type of second mortgage, or lien.
Used for: Borrowing money for any purpose desired by the homeowner, often home improvements or other major expenses. Fixed-rate, ARM, interest-only, balloon payment options.

A type of home equity loan in which you have a pre-set limit you can borrow against as needed. Usually divided into a draw period, during which you can  borrow money, followed by a repayment period.
Used for: Borrowing money at  irregular intervals for any purpose desired.  Draw period is usually an interest-only ARM; repayment usually a fixed-rate loan. 
Reverse Mortgage                              
A category of home equity loans for persons age 62 and above.     
Used for: Monthly stipends to supplement retirement income; monthly cash advances for a limited time; HELOC to draw as needed.

Taking out a new mortgage to pay off and replace an existing mortgage 
Used for: Obtaining more desirable loan terms than current mortgage offers, such as lower interest rate, lower monthly payments, shorter or longer payoff terms, replace adjustable-rate loan with fixed-rate loan or vice versa, among others. Options include fixed-rate, ARM, VA, FHA and USDA.
Cash-out Refinance                  
A single transaction to both refinance your current mortgage and borrow against your available home equity. 
Used for: Borrowing money for any purpose desired by the homeowner, in addition to any of the other potential uses of refinancing. Fixed-rate or ARM.
Harp Refinance
Government-backed program to help homeowners with low- and negative-equity (underwater) mortgages refinance to more favorable terms.  Stands for Home Affordable Refinance Program.   
Used for: Refinancing primary mortgages. 30-year, 20-year and 15-year fixed-rate options.   

FHA Loan    
Government program designed to facilitate home ownership.       
Used for: Home purchase, refinancing, cash-out refinance, home improvement loans. 30-year, 15-year fixed-rate, ARMs, HELOCS.

VA Loan  
Home loan program for members and veterans of the armed forces and certain others.    
Used for: Home purchase, mortgage refinancing, home improvement loans, cash-out refinance.  30- and 15-year fixed-rate, ARM.

USDA Rural Development Loan    
Program to assist low- to moderate-income persons purchase a modest home in rural areas and small communities.  
Used for: Home purchases, refinancing. 30-year fixed-rate mortgage only