A test suite is a collection of test cases. Just like we organize documents into folders, test suites help in grouping test cases.
You can categorize test suites based on functionality, module, environment, or something else. For example, you can have a test suite for smoke testing, a suite for API testing, a suite for mobile testing, and a suite each per module like a User module test suite, a Task module test suite, etc.
Test suites also help gauge the progress of underlying test cases during execution. For example, knowing that 90% of the API test suite is complete is a good indicator of the testing progress of the software's API.
In automated testing, a collection of test scripts is also called a test suite.