Time dilation, length contraction, and mass increase
One of the most shocking discoveries of Einstein is that time is not universal. If you were to fly on a spaceship at $99\% c$, your clock would tick much slower than a clock back on Earth. This isn't a mechanical error with the clock; time itself is moving slower for you. This is called Time Dilation.
As you speed up, not only does time change, but space does too! From the perspective of an observer on Earth, your 100-meter-long spaceship would actually appear to get shorter as it goes faster. At very high speeds, the ship might look like it's only a few meters long, even though you inside the ship feel perfectly normal.
The faster an object moves, the more "inertia" it has, making it harder to push. We often describe this as the object's mass increasing. As you approach the speed of light, your mass becomes nearly infinite, which is why it takes an infinite amount of force to reach the universal speed limit ($c$).
Why does all this weirdness happen? It’s because the Speed of Light must always be exactly the same for everyone, no matter how fast they are moving. To keep light's speed constant, the universe "bends" time and space to make the math work out. Everything in relativity comes from this one simple rule!