What is a database abstraction layer?
A database abstraction layer (DBAL) is a couple of functions or a class which deals with every aspects of database handling.
First of all you have a function to connect and to disconnect to/from the database. You also have some functions to submit a query, and to get the results and finally you need to have some error-handling functions too.
Why to use a DBAL instead of the regular php functions?
Of course you do not replace the php-functions, you just connect them to get a better performance when you need to develop your code, validate the data, etc.
If you use a really flexible DBAL, then you do not need to change every line of your code if you switch from one database type to the other.
How to write a DBAL?
Most users should not be writing their own DBAL, since there are several ready-to-use open-source DBALs available. One of the benefits of a DBAL is to make code more reusable, and writing your own DBAL (unless it achieves wide acceptance in the PHP community) is counterproductive. The most common one is the PEAR:DB package which is already installed on the majority of web servers.
You can find some less sophisticated DBALs in the source files of some well written open-source CMS sites also.