How does smart DNS proxy work?

When you use a smart DNS, this is what happens. Let's suppose that you are in UK but want to access a blocked site example.com in US (whose ip address is x.x.x.x).

1. You query the smart DNS asking to resolve example.com
2. As the smart DNS provider knows that example.com is a blocked site, instead of resolving it as x.x.x.x, it resolves it as y.y.y.y.

y.y.y.y is a proxy server of the smart DNS provider which is in the US. As a result you are connecting to example.com by using the Smart DNS proxy. In fact smart DNS are often called smart DNS proxy servers.