It sounds like what you're asking is about the concept of switched virtual interfaces - "interface vlan 10", for instance, is a switched virtual interface. This is different than a VLAN in that a VLAN is a logical network segment, a broadcast domain, whereas an SVI is a logical interface.
If SW2 is a layer 3 switch, you don't HAVE to have the SVI configured there. You could operate both SW1 and SW2 entirely as layer 2 devices, configure an interface on R1 to handle the inter-VLAN traffic, and configure the links from SW1-SW2 and SW2-R1 as trunks.
But that wastes the l3 capability of the switch. The idea is that you don't need to involve a router. When you have a vlan (layer 2), it has no way to communicate with other vlans (layer 2). That's where an SVI on a layer 3 switch, or an interface on a router (router-on-a-stick) using dot1q encapsulation comes in. It gives your devices in that VLAN something to point to as a gateway, something for routable traffic to address. So, think of a VLAN as a self contained network, and an SVI as the door that allows it to talk to everything else.
Also, in practice, assigning each discrete switch an IP address for management traffic makes things much easier - how else can you telnet/SSH into it? Beats having to use the console all the time!
HTH
