Imagine the hands on an analog clock. As the hands rotate, there is an invariant -- the length of the hand. We are completely unsurprised that as a hand on the clock rotates and becomes less horizontal, it must become more vertical. It can't both increase its "verticality" and its "horizontality".
Now imagine horizontal as space, and vertical as time. In this case a 2D spacetime, but we can't really visualize 4D.
The reason they always talk about space-time in relativity is that you can't separate the two. If you want to travel faster through time, you have to travel slower through space. If you want to travel faster through space, you have to travel slower through time. There's an invariant like the length of that rotating clock arm called the "spacetime interval" that remains constant under the transformations that you have to do to go from one observer's perspective to another observer's perspective.
Problem is its in 4D so it's hard to visualize. There is a mathematical framework that can explain all of the transformations leading to length-contraction and time-dilation as simple rotations in a 4D spacetime (3 space + 1 time). It requires a bit more math, but then unifies things in a conceptually simple way.
But maybe just remember:
"If you go faster through space, you go slower through time"
"If you go faster through time, you go slower through space"
Your maximum speed in space is the speed of light, at which others will observe you as having no time passing.
Your maximum speed through time is one second per second, at which others will observe you as being stationary relative to them.
Look up Alex Fluornoy's youtube video lectures. I'll edit this and link the specific one here later, if I can find it.