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Shutter speed is measured in seconds, and it means how much time will the shutter be open for. The longer the shutter is open, the more light reaches the camera sensors, and the brighter the recorded image is. It also works vice versa.
1/60 means the shutter is open for 1 over sixtieth of a second, which is nearly 0.02 seconds.
The typical shutter speeds range from 1/4000th of a second to 30 seconds. Although on some cameras there is up to 1/8000 of a second, and Bulb mode meaning the shutter will be open for as long as the shutter release button is held.
In photography we usually measure any amount less than a second as a fraction, but 0.3"(double inverted commas denote seconds, not inches) and above and the camera will show it as decimals.
Please feel completely free to ask any question, and the friendly CL community will try its best to answer!
P.S.: In Canon cameras, Shutter Priority mode is labelled Tv(and Aperture Priority is labelled Av), but on other brands it is normally labelled S(and A for Aperture Priority).