Permissions are the various capabilities a user can have on a Concrete CMS site. For instance, a user can have the ability to publish a page, delete a page, or even to view a page. Permissions can also apply to files, so that you can control how different users or users in different groups interact with those files and what kind of operations they can perform on them.
Sometimes, it is helpful to have an approval process when it comes to making changes on a concrete site - this is where Workflow comes in. You can set up a Workflow in a particular permission that can trigger a workflow that requires a user from a certain group to "approve" an action before it can occur, such as publishing a page with new changes.
Enabling "Advanced Permissions" on your site is a great way to get very powerful and granular control of how your users interact with your site.
To learn more about the various types of Permissions, visit the various Permissions sections in the Editor's Guide: