A digital computer's clock is a pulse generator which synchronizes operations throughout the system (or a portion of the system).
The higher the clock speed of a system, the more operations are performed per second. Performing more operations per second will usually lead to a more instructions being performed per second, but the relationship between the clock speed and instruction execution is rarely 1:1.
On CMOS processors (the majority of processors available today), each clock pulse leads to state change within the processor, and therefore to energy consumption. The higher the clock rate, the more energy is consumed, and the more heat is generated.
A clock cycle is the activity provoked by one clock pulse (and the length of time between pulses).