An internet exchange point (IXP) allows its members to exchange traffic destined to each others network at a very low price. It encourages the use of local resources and reduces the load on the global Internet. Each member connects to the peering point and agrees to allow other members to transfer to and from their local network.
The exchange itself is usually a simple layer-2 infrastructure like an ethernet switch to which all members connect directly from their routers. To know about the other networks attached to that infrastructure the members use a routing protocol, usually this is BGP4 (Border Gateway Protocol Version 4).