On a Macintosh the control key has two main uses.
Firstly, when using the mouse, if you hold down the control key while you click the mouse it gives you a contextual menu – a mini menu related to what you are doing at the time. Try it now – hold down the control key and click somewhere in this window. A menu will appear! This is exactly the same as a right-click with the mouse. The control key was more important in the days when Apple computers just had a one button mouse.
Secondly, there are some special keypreses that involve the control key. Here are some that I find handy:
Control- F4 cycles between your open windows.
Control-option-apple-eject (The left three keys on the bottom row of the keyboard, plus the top right key) will immediately shut down your computer – no questions asked. This is the fastest way to turn off your mac.
Control-shift-eject puts your display to sleep.
If you hold down control while doing a screenshot (shift-apple-control-3) it will copy the screenshot to the clipboard instead of saving it to your desktop.