Your router is, at it's core, a very advanced traffic cop and NAT – Network Address Translation – is it's primary function. You have multiple devices on your local network (LAN) that need to communicate with other non-local servers via the WAN (i.e. the internet).
Now you have a problem. Your ISP assigns you (usually) a single IP address on their network which is on a different subnet than your LAN. Devices on your local network and devices on the WAN are not aware of one another and cannot communicate with each other directly. So, requests have to be routed to the correct destination via your router.
SRC-NAT
Let's say you're trying to pull up a website on your computer. Your computer sends the request to the router. Your router alters the IP packet headers so that the request source address, and therefore the address that the server responds to, is your WAN IP instead of the requesting devices LAN IP. Your router then forwards the packet to the destination server, tracks the connection, and forwards the response back to your computer.
DST-NAT
Let's say you're hosting a web service on your home server that you want to make available publicly. You would set up a dst-nat (often called port forwarding) rule in your router/firewall which will tell your router to redirect any requests received at the WAN IP on port 80 or 443 to your home server's IP address. Unlike SRC-NAT, your router doesn't replace the source IP address. Just the destination. Your server knows that the requesting device is not on your LAN subnet and will forward the response back to the gateway (your router) which is already tracking the connection and will forward the response back to the requesting device via the WAN.
Routing DNS with DST-NAT
Since DST-NAT is just changing the destination IP address and routing the packet to the new destination, this can be done internally in some situations as well. To redirect DNS requests, you would set up a rule in your router/firewall to grab outbound UDP packets that originated from the LAN, do not originate from your internal dns server, and have a destination of port 53 and redirect/dst-nat them to the IP address of your choice. The new destination can be an internal or external IP address and the requesting device won't know the request was redirected.
OpenWRT's documentation actually has a section that deals with DNS redirection which you can find here. The DNS redirection part is near the bottom of the page.
NAT TLDR
Your router is, at it's core, a very advanced traffic cop and NAT – Network Address Translation – is it's primary function. You have multiple devices on your local network (LAN) that need to communicate with other non-local servers via the WAN (i.e. the internet). Now you have a problem. Your ISP assigns you (usually) a single IP address on their network which is on a different subnet than your LAN. Devices on your local network and devices on the WAN are not aware of one another and cannot communicate with each other directly. So, requests have to be routed to the correct destination via your router.
SRC-NAT
Let's say you're trying to pull up a website on your computer. Your computer sends the request to the router. Your router alters the IP packet headers so that the request source address, and therefore the address that the server responds to, is your WAN IP instead of the requesting devices LAN IP. Your router then forwards the packet to the destination server, tracks the connection, and forwards the response back to your computer.
DST-NAT
Let's say you're hosting a web service on your home server that you want to make available publicly. You would set up a dst-nat (often called port forwarding) rule in your router/firewall which will tell your router to redirect any requests received at the WAN IP on port 80 or 443 to your home server's IP address. Unlike SRC-NAT, your router doesn't replace the source IP address. Just the destination. Your server knows that the requesting device is not on your LAN subnet and will forward the response back to the gateway (your router) which is already tracking the connection and will forward the response back to the requesting device via the WAN.
Routing DNS with DST-NAT
Since DST-NAT is just changing the destination IP address and routing the packet to the new destination, this can be done internally in some situations as well. To redirect DNS requests, you would set up a rule in your router/firewall to grab outbound UDP packets that originated from the LAN, do not originate from your internal dns server, and have a destination of port 53 and redirect/dst-nat them to the IP address of your choice. The new destination can be an internal or external IP address and the requesting device won't know the request was redirected. OpenWRT's documentation actually has a section that deals with DNS redirection which you can find here. The DNS redirection part is near the bottom of the page.