Click the little arrow to the right of a task title to open/collapse its subtasks.
How to collapse/open multiple tasks
You can also collapse/show the subtasks of all the tasks in the day view by holding shift and clicking the arrow on one of the tasks.
Showing completed subtasks
Hold Alt (Option on Mac) and click the arrow to show or hide the completed subtasks of that task. This temporary toggle works the same way as Alt+clicking project arrows elsewhere—it shows or hides completed items just for that moment without saving a preference. See Showing completed tasks: inline, in a section, or hidden for details about this Alt+click behavior and how completed items are managed across your tasks and subtasks.