The thought experiment that illustrates time dilation in special relativity is the twin paradox.
In its classic form, one twin travels through space at a speed close to light speed while the other remains on Earth. When the travelling twin returns, less time has passed for them, so they are younger than their stay-at-home sibling. This difference is called differential ageing.
The apparent paradox comes from the fact that each twin can see the other moving during part of the journey. The situations are not truly symmetrical, however: the travelling twin changes inertial frames when turning around, while the Earth-bound twin remains in one frame. Relativity of simultaneity also affects how each twin calculates the other's age.
The idea traces back to discussions following Einstein's 1905 paper; Paul Langevin developed a famous version in 1911. The effect is experimentally supported by precise atomic clocks and even affects astronauts in orbit.