What does the time dilation equation t=t(p)*γ mean and when do you use it?

[Dgonzo15]

Hello, can someone give me an explanation of the time dilation equation t=t(p)*γ? I know it's used to measure something about a difference in sense of time in different reference frames, but I don't know how to put it into context. Can someone give me an example where you would use the time dilation equation?

 

[Janus]

Assume you have two clocks that are identical in construction.

Assume clock A is moving at 80% of the speed of light relative to clock B.

This would make γ equal to 1.6666...

t(p) would be the time that passes on clock A as measured by clock A

t is the time clock B measures for that time to pass on for clock A.

For example after 1 hr according to clock B, only 0.6 hrs will have passed on Clock B.

This assumes that the "observer" is at rest with respect to clock B.

 

[Henriamaa]

Simple example, I am on the Earth with a clock that has been synchronized with another clock at some common origin (second clock on a plane moving past me at 50% speed of light). If I want to know what the clock reads on the plane in my reference frame, I have to use time dilation equation.