Tire tread thickness is measured in 32nds of an inch. Legal minimum tread depth in most states is 2/32 of an inch, measured at certain spots around the tire. The tread depth is what allows liquids, dirt, mud and snow to be pushed and/or pulled away from the contact portion of the tire, allowing the tire to better grip the road surface. Most passenger car tires have brand new tread depths of about half to 20/32 of an inch. This is the measurement of the groove, or valley on your tire. The deeper this groove is, or the thicker the tread is, the more liquid, snow or mud can be channeled away from the contact portion of the tire. Meaning increased safety in inclement weather or hazardous driving conditions.
For more info, see How to Check Your Tire Tread