In the study of waves, frequency and period are related because each is an inversion of the other. Frequency is a measure of cycles per second, while period is a measure of seconds per cycle.
Frequency is a measure of vibrational cycles per second, and is measured in Hertz (Hz). One Hz is one cycle per second, two Hz is two cycles and so on. The higher a wave's frequency is, the more vibrational cycles occur each second. This essentially means that a medium carrying a wave with a high frequency will vibrate faster than a medium carrying a wave with a low frequency.
Period is similar to frequency, but it is not the same. Rather than cycles per second, period measures the seconds per cycle, or how long it takes for the wave to complete one vibrational cycle. Where frequency is a measure of how often a cycle occurs, period is a measure of how long it takes for one cycle to occur. This means that period is simply a measure of time, and is often measured in seconds.
Because a wave's period is the inverse of its frequency, the period can be found if the frequency is known and vice versa.