Note: While there is a feature called Session debug logging, this section is about the system log and how to use logging within scripts effectively for troubleshooting your code.
Logging is something that you can employ both server-side, and client-side. There are several useful logging API methods that can be employed for various purposes, and in different situations: info(), warn(), and error(), each with respectively higher levels of significance. These three types of logging methods are available both from the GlideSystem API (available within all server-side scripts as the gs object) on the server, and from the console API on the client.
An informational message (using gs.info() on the server, or console.info() on the client) is meant to inform a curious admin perusing the logs, of some important state information, or perhaps about successful execution and final state of a particularly complex script...