Imagine your network card is a house. That house has an address (IP address in this case) and to get into the house you need doors (ports). The house is pretty big so it has exactly 65,535 doors (ports). But because the owner of the house is not insane, most of the doors are locked (firewall).
When something communicates with you (or you with something), you use a port. For example when you open a webpage, your browser sends a request to the server on port 80 or 443 (80 for http, 443 for https). Those are standardized ports which have a well-defined meaning, but in general you only need the client (browser, app, whatever) and server to use the same port for the service.