Time Dilation....what it means

[Master J]

I am trying to get my head around some of the basics of relativity.

dt' = ydt

Where dt is the time between 2 events in frame S, and dt' is the time betwen the same events in frame S', that is moving witha constant velocity relative to S.

What exactly does this say? Does it mean that the observer in S' will measure a greater time interval than in S, or that the observer in S will see the time interval in S' as longer than his?

Like if it means that the observer in S' will measure a greater time interval, well howcome the observer in S doesn't, since one could equally say that he is moving relative to S'?

I hope you guys can sort this out, its just tricky to get the hang of.

[Ich]

Like if it means that the observer in S' will measure a greater time interval, well howcome the observer in S doesn't, since one could equally say that he is moving relative to S'?
The formula is valid only if the two events happen at the same place in S, not in S'. It says that in this case, S' measures a longer time between the events than S, since y>1. Generally, the observer for which the two events happen at the same place measures the shortest time.