Period is the time it takes for something to happen once.  It is given in some unit of time, like seconds or days...

EXAMPLE: Earth's peroid of rotation is one day.  (T=1day)

Frequency is how often something happens.  The time unit goes on the bottom of the fraction, or it is written with a negative exponent...

EXAMPLE: Earth's frequency of rotation is 1/day.  (Same as 1day^-1)
If you read this sentence out loud, you'd say, "The frequency is once per day."

We most frequently use "/s" as our frequency unit.  In honor of a famous researcher, many refer to "/s" as Hertz.

EXAMPLE:  A strobe light flashes 20 times per second....

  f   =   20s^-1   =   20/s   =   20Hz

I prefer to see it as 20/s, but to each his own.

Period and frequency are closely related.  Since T is total time, and frequency is the reciprocal of this, we can say that...

T = 1/f

f = 1/T

Now we can interchangeT or f into any other equations to suit our needs.