Test plans are indeed basically a collection/group of related test runs. When you create a new test plan, you can select the test suites on the right sidebar to include (by clicking on the icon right to a test suite). So, for example, when you include three test suites in your test plan, this will effectively result in a test plan with three test runs.
When you view a test plan, you can see the individual test runs and the aggregated statistics of all test runs.
Test plans get especially interesting if you need support for so called configurations (for example, different operating systems, browser versions etc). You can specify multiple configurations for a suite in a plan and TestRail automatically creates a test run for each configuration combination.
I know that the documentation is currently not explaining any of this and we will have a more complete documentation when TestRail launches.
Regards,
Tobias