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I believe it's a way to remotely access a server/pc and run commands
That's right, here's wikipedia for more info: http://en.wikipedia.org/wiki/Secure_Shell
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Actually, it's a secure version of rsh (Remote SHell).
As you get farther into Unix, you'll hear about "r" commands and "s" commands. The r-commands are remote copy (rcp), remote shell (rsh), remote login (rlogin). Great commands, except that they're clear text, so your passwd is exposed.
The "s" commands are secure replacements for the "r" commands, encrypting all the communications.
Right. SSH requires users and machines to have public and private encryption keys. In order to jump from one machine to another, a key must (1) be listed as an acceptable key on the remote machine and (2) a password must be entered. On successful validation, you'll have an encrypted connection between both machines.
This is a major improvement over rsh for a number of reasons--prevents a man-in-the-middle attack, spoofing a machine's identity, etc.--and is now the de facto standard.