There are two definitions for a backdoor but both perform the same function. The function of a backdoor is to allow an unauthorized user to get access to one or more computer resources. It bypasses normal authentication processes to allow access to be secretly obtained by one or more unauthorized users.
A backdoor may be a part of a program created by the author of a program which allows the author or someone else to gain access to the computer program or computer system the program is running on.
A second slightly different definition of a backdoor is a program which is specifically written to allow an unauthorized user to have access to a victim's computer. This is considered a hacker tool used to maintain control of a victim's computer.
Sometimes backdoor functionality may be inserted into a compiled version of a program but not included in the human readable program code.