Squirrel classes are internal classes from the server or client exported to Squirrel scripting. These can be for example in-game entities or data storage classes, such as hash tables. Unlike many other languages, in Squirrel the objects of these classes also act as real objects, which means you can return or modify the class properties (such as health for a player), or use built-in method functions to execute more complex tasks.
The following is a complete list of classes bound to Squirrel scripting. In addition to these, there are also script types which are basically classes without any methods, and they're meant to add extra functionality and ease of use to scripting.