I get time dilation - a hypothetical clock consists of two parallel mirrors with a photon that bounces between them. The photon makes the round journey in 1 second. If the clock is moving, the photon travels in a diagonal path - a longer distance -and it therefore takes longer to bounce between the mirrors. Therefore, from our perspective, each second on the moving clock is thus longer than on the stationary clock.

What I don't get is how, even though both clocks are experientially (if they were conscious) living the same amount of time, the moving clock returns "younger" (if we say the moving clock's velocity was close to the speed of light).

This is probably a really dumb question, but I literally started researching physics today.