Slots (with the little clips on the right hand side) are for PCIexpress graphics cards. You have two, so your system is capable of running 2 cards in SLI mode (scaleable link interface) This adds graphic performance, and is very good for gaming.
You need to ensure that your power supply is adequate if you intend to use two cards. (minimum 600 watts and some cards need more. You also need seperate power connectors for each card in most cases.
The shorter slots are for other pcie devices which are appearing such as network, wireless and infrared devices.