First, a quick rundown of the anatomy of a yo-yo: two disks of equal size are placed together and connected with a little part in the middle called an axle.
A string is affixed to the yo-yo, either by tying a loop around the axle or by attaching the end of the string directly to a point in the axle.
A yo-yo is able to “sleep,” or stay spinning at the bottom of the string, because as the string loops around the axle, gravity keeps it down instead of winding the yo-yo back up.
The axle has to be smooth enough that it can spin freely in the loop of the string, yet has to have just enough friction that when you jerk the string, the axle will grip it and wind back up.
When you want the yo-yo to come back up, a simple jerk will begin the process of the string wrapping around the axle. Of course, none of this works at all the yo-yo will not “sleep” if the string is affixed to only one place on the axle.