A VPN will provide a secure tunnel between the device running the VPN client (your dd-wrt router) and the VPN server (hosted by your VPN provider). All traffic that gets routed through the tunnel will be reasonably secure against monitoring and tampering, but only while its in the tunnel.
On either end of the tunnel, it is still vulnerable. The VPN provider will be able to monitor all of the traffic as it passes in and out of their end of the tunnel, just as your dd-wrt router will be able to monitor the traffic as it passes in and out of its end.
A VPN is only useful if:
- You trust the network and/or device running the VPN client
- You trust the VPN server
- The adversary you wish to protect yourself from is thought to be somewhere between the two
The same goes for HTTPS and anything else that uses SSL/TLS.