DHCP (Dynamic Host Configuration Protocol ) is a communication protocol that is used to coordinate a network via a server. The server in most home cases is your internet router. It coordinates the network.
Think of your network as a town with streets, every street has a unique name aka network address. So when a new device gets into the town it gets a unique address in a certain format, when requested by the clients. Mostly IPv4 i.e. 192.168.178.20.
Second there are ports. Ports are the house numbers of the streets. So if two devices use the same IP they still can be differentiated by using different ports. To address a specific port you write it behind the IP, in our example 192.168.178.20:80. So we use port 80.
To come back to the beginning the router coordinates the IP addresses and the ports from your internal network via DHCP and makes sure every device is accessible and no doubles.
There is a lot more but very briefly this is it.
You are correct, there is a lot more to dive in like NAT, IPv6, static or dynamic address, UPnP, MAC address, subnet space etc.
But I wanted to keep it simple.