Safe Modules enable additional access-control logic for your Safe. Essentially, every Safe is controlled by two means. By the account owners using their signer keys and by optional modules that have their own custom access logic.
So, for example, you could have a Safe that is controlled by 3 out of 5 owners and an additional module that allows an admin key to control the Safe with just one single signature.
This already highlights that Safe Modules are very security-critical and should only be added by advanced users that fully understand the security implications.
Besides an admin key, modules can also be used to enable:
Hierarchical account access
Direct execution of DAO decisions
and much more...
Other than Spending Limits, we don't currently support any official modules in the Safe application. But modules can also be built by third-parties and complimented with a Safe App as a UI to the module.
Read about how you can add a third-party module in this article.