When you originally applied for and got your mortgage approved to purchase the home you signed a mortgage note and a deed of trust.
The mortgage note and deed of trust stated that the bank could put a lien on your home and listed the loan terms as well.
When you pay off the mortgage in full you should receive some documents and the deed and original note should be sent back to you from the bank once your mortgage is paid in full.
Although some banks won't automatically send you the documents and in some cases you may have to contact the bank yourself to get them to send you the documents.
The bank should also be removed from the Real Estate Taxes and Home Owners Insurance which is important so that you'll be the only one listed on the Taxes and Home Owners Insurance so you can take care of things with the insurance company should your home be destroyed and you need to put in an insurance claim.