For AMD based systems PCIe 3.0 means nothing. AMD does not currently have a chipset that supports PCIe 3.0.
PCIe 3.0, compared to PCIe 2.0 is, for the most part, a difference in available bandwidth per lane and reduced overhead for communications. There are, of course, other underlying differences but they don't have a noticeable impact on consumers.
PCIe communication bus is split into lanes. Each lane carries a certain amount of data as defined by the applicable spec. For each expansion slot, you have from 1 to 16 lanes depending on the exact expansion slot. A PCIe controller with 32 lanes (PCIe x32) allows for 2, PCIe x16 slots or any combination of expansion slots totaling 32 lanes.