These are cargo vessel size categories. Capesize refers to dry bulk carriers that are too big to pass through the Suez or Panama canals. Consequently they have to go round the southern tip of Africa (Cape of Good Hope) or South America (Cape Horn). They are usually around 80,000-160,000 deadweight tons but can be larger, and typical cargoes are iron ore and coal. Needless to say they require deep berths or trans-shipment facilities on arrival.
Panamax cargo ships are the largest that can go through the Panama Canal, and are usually about 65,000 dwt. Handymax vessels typically carry dry bulk cargoes like steel, are in the 35,000-60,000 dwt range, and are equipped with on-board cranes. . And for more detail click and see this, this and this Wikipedia entries.