Port numbers are integers in the range 1-65535 used to distinguish between different services offered by a given machine on the internet.
Each internet machine has one space of 65535 port numbers for TCP connections and a second, separate space of 65535 port numbers for UDP connections.
These port numbers form the only way of distinguishing between different processes or users on the same machine using the UDP and TCP Internet protocols: An internet IP address (128.95.44.22, say) plus a port number form the most specific Internet address these protocols understand.
Reference:
A Firewall Engineer 