Tests can be simple one-liners or extremely complex issues with a lot of detail, steps, links and files associated with them. In either case, once a test has been created, the next logical thing to do is execute it. Executing a test means providing a high level status on what happened when the test was "run" or "executed" and doing some follow-up actions on that (like filing a new bug, linking an existing one, attaching screenshots, making notes, etc).
Test executions can happen in many ways. Based on how the testing process for your project is set up, you can be executing tests in one of the following ways:
Create a test and execute it right away in an ad-hoc manner.
Create a Test Cycle, create a test and execute it right away as part of that cycle.
Use Quick Execute feature to change the execution status from the Test Cycle list or View Issue page.
Search for test executions and execute them from the resulting search result set, both in the List View and Detail View.
Combinations of the above are possible but it is important to pick a certain process and stick with it for the duration of the project or a version in order to gain efficiencies in the execution and test reporting process.