Permission Sets make it easier to apply a group of permissions to specific users. You can create a permission set here that defines what access the user will have to which it is applied. The three listed below are the default "out of the box" permission sets but you can edit or delete these and also make your own.
For example, if you wanted to create a permission set for your developers that build your applications, you might create a permissions set called, "App Developers" and select the sections that they would need access to when building API integrated applications.
The System-Wide option just means that this permission set will be available in accounts across the system to apply to users. It does not mean that the user it is applied to will have System-Wide access.
The Account-Wide option just means that this permission set will be available in all groups in the account to apply to users. It does not mean that the user it is applied to will have Account-Wide access.