This law states that if object A is in thermal equilibrium with object B, and object B is in thermal equilibrium with object C, then object C is also in thermal equilibrium with object A.
+-----+-------+----------+
| | | |
| A | B | C |
| | | |
+-----+-------+----------+
So if A and B are in thermal equilibrium (same temperature with no heat transfer) and B and C are also in thermal equilibrium, A and C can be brought in contact with one another, and there will be no heat transfer. More simply, this means that all three are at the same temperature.
This law is called the "Zeroth" law because it logically precedes the First and Second laws, though it was formulated later.
Sources
http://www.taftan.com/thermodynamics/ZEROTH.HTM
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thereq.html#c2