This is a global command which will enable Layer 3 routing on your switch. This will allow communication between VLANs on that switch through Layer 3 protocols.
Daryl and Joseph make important points. I would like to approach the answer from a different perspective. Before using ip routing the switch is forwarding using only layer 2 information. For every frame entering the switch it looks at the destination mac address and determines how to forward toward that mac address. After enabling ip routing the switch is forwarding using both layer 2 and layer 3 information. Now when a frame enters the switch it will check the destination IP address and if it is remote it will look for a next hop to use in forwarding. If the destination IP address is local then the switch will look at the destination mac address and look for a way to forward toward that mac address.
The other important change is that when configured as a layer 2 switch the switch used its configured default gateway to forward packets originated by the switch. When IP routing is enabled the switch stops using its configured default gateway and begins using any IP routes that it has (could be static routes configured or dynamic routes leaned from a routing protocol).