Every computer and network device attached to the Internet has at least one IP address. For example, the IP address of this web server is 126.96.36.199.
Then, within each of those IP addresses, each computer and network device will have a number of TCP ports. For example, the web server software on this web server responds on TCP port 80 and the mail server software on the same computer responds on TCP port 25.
In a non-technical sense, you can think of an IP address as the address of an office building and the TCP ports are individual offices within that building.
TCP ports either originate connections or they receive connections. Any TCP port can originate a connection, and the port numbers for those are not important. TCP ports which receive connections, on the other hand, have to be assigned specific port numbers so that people and applications know where to look for them. For example, DNS answers on TCP port 53 and HTTP answers on TCP port 80.
Port numbers that are statically assigned are known as “well known port numbers” and are usually below 1,024. To see a list of well known TCP ports, read What port number is XXX on?.