On a 1 GHz processor, the system clock "ticks" one billion times per second. Processors with gigahertz-based (GHz) clock speeds are measured in billions while processors with megahertz-based speeds (MHz) are measured in millions.
A processor cycle is the time it takes to send a single pulse. A pulse consists of a high followed by a low voltage signal, which is also called the tick and the tock. The number of ticks, tocks and cycles per second are all the same, although each cycle consists of a tick and a tock. The high and low voltage signals are representative of the 1's and 0's used in the binary system.
The speed of the processor is determined by the resonance of a vibrating crystal, usually quartz, in the crystal oscillator that's found in most electronic devices.