ssh is short for Secure SHell. It allows a user to log from their local computer into a remote computer anywhere on the internet. It is a more secure replacement for telnet.
On Linux or Mac, SSH is usually pre-installed. Most people are using OpenSSH from the OpenBSD folks. GNU has its own version, known as GNU lsh. There are various applications that support SSH on Windows.
SSH servers can accept passwords, or SSH Key Pairs for authentication.