User Defined Function, or UDF is an extension to a SQL database server (like MySQL) that can be compiled for use in a SQL query. For example, if it is necessary to obtain a random number for use as a primary key, and MySQL does not support that function, a new, external function could be written and compiled to accomplish this task. One sample of such query could be:
SELECT GETRANDOMKEY();
Essentially, this external function becomes part of the server itself.
For specific information pertaining to UDF's in MySQL, visit the MySQL website at [1]