In the simplest usage, "nc host port" creates a TCP connection to the given port on the given target host. Your standard input is then sent to the host, and anything that comes back across the connection is sent to your standard output. This continues indefinitely, until the network side of the connection shuts down. Note that this behavior is different from most other applications which shut everything down and exit after an end-of-file on the standard input.
Netcat can also function as a server, by listening for inbound connections on arbitrary ports and then doing the same reading and writing. With minor limitations, netcat doesn't really care if it runs in "client" or "server" mode -- it still shovels data back and forth until there isn't any more left. In either mode, shutdown can be forced after a configurable time of inactivity on the network side.
And it can do this via UDP too, so netcat is possibly the "udp telnet-like" application you always wanted for testing your UDP-mode servers. UDP, as the "U" implies, gives less reliable data transmission than TCP connections and some systems may have trouble sending large amounts of data that way, but it's still a useful capability to have.