What is SAPI and when would you use it?

I've been learning about error handling in PHP recently and came across the error_log() function.

In the PHP manual, it talks about all the error log types and I understand all of them except for type 3 which states that the error message is sent directly to the SAPI logging handler. My question is what exactly is SAPI and when would you want to use it?

SAPI stands for "Server API" (and API stands for "Application Programming Interface"). It is the mechanism that controls the interaction between the "outside world" and the PHP/Zend engine. So, you would always want to use it. In fact, you cannot avoid using it without a lot of effort since even CLI is considered a SAPI.