I know this thread is almost a year old but I was wondering the exact same thing as the OP and when I did a search this thread came up so I thought id take the time to comment on a few of the answers.
1) If your internet provider is like mine (suddenlink) and you type a invalid URL it redirects to a suddenlink ad page that generates them money. I don't know about you, but after the $160 a month i already pay and the data caps and add-ons for every little thing like unlimited data, data plan speed, etc i would rather not give them another penny so a alternate DNS server is a great solution to this.
2) Using a program like DNS Benchmark by Steve Gibson is a great tool to find a faster DNS server to use so not only do I avoid the redirects for ad pages, I also have a faster DNS resolver.
Also, Im not positive but from what I read you don't want your client DNS address to be the same as your router gateway (typically a private address like 192.168.1.1, etc) because its one more thing the router has to process. Its better to have the client use the LAN DNS address that you specify in the LAN DNS setting, which I come up with by running the DNS Benchmark program and then using the 2 fastest nameservers from there and entering them in the WAN DNS settings in my router, but I enter the fastest DNS resolver in the second box and the slower one in the first box. Then I put the same address I used for the second DNS address in the WAN DNS settings for the LAN / DHCP / DNS setting in the router. The reason I do this is that the router (asus anyway) always adds on the gateway address as an additional DNS address after the one you specify in the LAN DNS setting which tells me (again I could be wrong) is that you would want your fastest DNS server in box 2 of the WAN DNS settings so if the first one is down the router will default to the WAN DNS server primary which is really your second fastest DNS resolver. Does that make sense?