What is the role of layer 3 routing and layer 2 switching in a computer network?

Simply, L2 switches support  L2 Vlans, so it is just divide the network into separate broadcast domains by creating Vlans, it does not participate in L3 routing, not intervlan routing and no SVI

 

L3 switches, support SVI in order to participate in routing and hence intervlan routing can be done on L3 switch instead of a router

Layer3 Routing is for selection of best path for packets to be routed over internet cloud, while Layer2 switching serves for your small network within a building or room.