Apex Scripts is a MavensMate-specific feature. Simply put, it allows users to create named Apex scripts that can be run inside Sublime Text.
Creating Apex Scripts
To create a new Apex Script, select
MavensMate > New Apex Script and enter a name for your script (or you can use the Sublime Text command panel).
Running Apex Scripts
To run an Apex Script, with the Apex Script open in a Sublime Text tab, select
MavensMate > Run Apex Script. This will run the Apex in your script via Execute Anonymous and return the debug log to Sublime Text.