There are a couple of things to understand here.
IP addresses
Your home router generally allocates IP addresses for all the connected devices on the home network. The addresses are often in the 192.168... range, and are only unique on the local network. Millions of local networks will all be using the same local IP addresses.
The router usually also has a connection to the Internet, and when seen from the Internet it will have single unique address - often referred to as its "public IP address". This address is unique, so someone could sent a request to this address, and it will end up at your router. But from there, your router needs to know which local IP address it needs to send it to - that's where "port forwarding" comes in.
In the router's configuration you need to set up rules about what to do when an inbound request arrives on a given port. For example:
port 80 -> forward to 192.168.1.50. Any requests on port 80 will be forwarded to IP address 192.168.1.50 on the local network.
There are a few things to consider. You don't want IP addresses changing or this will solution stop working. So generally you will also configure the router to always give that device the same local IP address - this is known as a "static" IP address. Similarly you also want your public address to be the same... if you restart your router you may be assigned a different public IP address. Your ISP can usually (not always) assign a static IP to ensure you always get the same public address.
Domain names
This is just a nicer way to point to an IP address. You can register a "domain name" and then use that instead of the public IP to connect to a service on the Internet. So www.google.com instead of 172.217.24.36 for example.
Sometime an ISP is not able to provide a static public IP address, so that's where "dynamic DNS" comes in. Basically you register in a similar way but this time if your IP address changes then you tell the Dynamic DNS that is has changed so it continues to work even with the new public IP address.
This is a very simplistic view of things, but hopefully gives you an overview.