What is a time period

There are many meanings depending on what you are doing.

I have a sneaking suspicion that you are working with simple harmonic motion of a pendulum or spring and mass or something. In that case it is the amount of time that it takes for the argument of the trig function to change by 2 pi or in other words start over.
for example if you have a function like
y = A sin ( 15.4 t + 3.787)
then how long does it take for that to be
y = A sin (15.4 t + 3.787 + 2 pi) ???
well it is when
15.4 (t+T) = 15.4 t + 2 pi
or
15.4 T = 2 pi
T = 2 pi/15.4 = period