What does "active test configuration" mean? Is it a subscription?

No, it isn't a subscription. You're licensed for life, for the current major release version. (When there's eventually another major upgrade, e.g. to version 4.0, that'd likely be a paid upgrade... but you don't have to upgrade, of course.)

A "test" is a configuration or setup, containing a URL, location, or other attributes. Basically saying what to look for.

A "check" is what Simon does with a test: it periodically runs the test to see if it is successful or a failure, and optionally if it changed.

If you have a license with 40 active tests, that means that you can have up to 40 tests that are not paused. It doesn't count paused tests. Each test can be checked any number of times; there's no limitation on checks.