In really simple terms: you run PuTTY on a Windows machine, and tell it to connect to (for example) a Unix machine. PuTTY implements the client end of that session: the end at which the session is displayed, rather than the end at which it runs. These protocols are all used to run a remote session on a computer, over a network. PuTTY is a client program for the SSH, Telnet and Rlogin network protocols.
PuTTY is a free implementation of Telnet and SSH for Windows and Unix platforms, along with an xterm terminal emulator.