How can time change along your speed?

I'm following on Youtube some Physics channels ( they worked on the CERN) and one of them told in a recent video that time is dfiferent depending of your speed.

From my understanding, we measure time with the numbers of oscilation made by and isotope of Cs on certain conditions. So, how does speed change the way we measure time? Should not it be the same here on Earth than in a planet/star/X that travels, for example, at 9/10 of the speed of light?