By assigning tasks to members, you let them know which tasks they should be working on. 

The members could use timelogsonly for tasks you assigned to them.

For adding members to a task, click the task to open it, and then choose "Members" from the right side of the modal or press the "M" button.

Type the member's name or just click on their avatar

You need managing access to assign tasks.

For assigning tasks to yourself, just keep the cursor on the task and press the spacebar.