The user guide says "When working on a task, click the Checkout button. This prevents anyone else working on the task at the same time." (You may want to modify the grammar)
When I check out a task, another user is able to modify the task and complete and uncomplete the task. There is no difference besides noting that I have it ‘checked out’. In order for checkout to have any effect as far as I can tell, the home section has to be refreshed by others when someone checks out a task.