What is a mortgage?

A loan secured by residential property.

Colloquially, a mortgage is a loan secured by residential property. Mortgages are also commonly referred to as "home loans." 

Technically speaking, a mortgage is a legal document (see Deed of Trust) between a mortgagor (e.g., a bank) and a mortgagee (e.g., a borrower) that establishes a home and/or property as security for a home loan.