As the name suggests, Panamax vessel is the largest size of the vessel that can transit the Panama Canal.

The maximum size of the vessels allowed in Panama Canal is

• Overall Length:  950 ft (289.56 m) with few exceptions for container vessels and rigidly connected tug-barge combination
• Max Beam: 106 ft (32.31 m)
• Max Draft: 39.5 ft (12.04 m) in Tropical Fresh Water (TFW)
• Max Air Draft: 190 ft (57.91 m) measured from the waterline to the vessel's highest point

A ship of these dimensions would typically have deadweight between 65000 to 80000 T. 

Now with the expansion of the Panama Canal, there is new term for size of the ship, which is called "new Panamax".