Every device connected to a network has an IP address — a way to be found. A port is a number, from 1 to 65535, that identifies a specific service or application running on that device. If the IP address gets data to the right computer, the port gets it to the right program running on that computer: web traffic to the web server, mail to the mail server, and so on, all sharing the same IP address without interfering with each other.
Ports work with either of two protocols. TCP (Transmission Control Protocol) sets up a reliable, confirmed connection before any data flows — used by web browsing, email and file transfer. UDP (User Datagram Protocol) sends data immediately with no setup and no confirmation of delivery — used where speed matters more than guaranteed delivery, like DNS queries, VoIP calls and many online games. A service is the software listening on a given port for that traffic; client/server communication is simply one device (the client) connecting to a specific IP address and port on another (the server) to use that service.
A handful of ports are reserved by convention for well-known services: port 80 for HTTP, 443 for HTTPS, 22 for SSH, 25 for SMTP, 53 for DNS, and 3389 for Remote Desktop. See the full reference table further down this page.