For intuition I find it easier to start with a regular pendulum. Imagine a steel ball on a string hanging down. If you give it a push, it will start to swing back and forth.

Now if you, while the pendulum is swinging, give it another push in the same direction, it will matter where it is when you push it. If it is travelling in the opposite direction you are pushing it in (say, you push from left to right, then this would mean pushing when the pendulum is travelling right to left), you will slow the pendulum down. However, if you push it, when it is already travelling in that direction (so, push it from left to right when it is already travelling left to right), it will speed up.

Now say you push it periodically, that is, in regular time intervals. If you just choose a random interval to push the pendulum, you will sometimes push it to make it go faster, and sometimes to slow it down. Depending on the exact frequency you push it at, this will mostly cancel out.

If you, however, push it always when it is going left to right, it will speed up every single time you push it. But in order to push it at the same point in its period, the frequency you are pushing it in must match the frequency the pendulum is going in anyway. This frequency is called the natural frequency or resonant frequency of the system (there are nuances between these terms that don't matter in this context). So pushing at that frequency will lead to resonance and (without damping) the pendulum will swing higher and higher (its amplitude will become arbitrarily large).

The same is true for larger and more complicated systems, though they will ususally have multiple resonance frequencies.

For intuition I find it easier to start with a regular pendulum. Imagine a steel ball on a string hanging down. If you give it a push, it will start to swing back and forth.

Now if you, while the pendulum is swinging, give it another push in the same direction, it will matter where it is when you push it. If it is travelling in the opposite direction you are pushing it in (say, you push from left to right, then this would mean pushing when the pendulum is travelling right to left), you will slow the pendulum down. However, if you push it, when it is already travelling in that direction (so, push it from left to right when it is already travelling left to right), it will speed up.

Now say you push it periodically, that is, in regular time intervals. If you just choose a random interval to push the pendulum, you will sometimes push it to make it go faster, and sometimes to slow it down. Depending on the exact frequency you push it at, this will mostly cancel out.

If you, however, push it always when it is going left to right, it will speed up every single time you push it. But in order to push it at the same point in its period, the frequency you are pushing it in must match the frequency the pendulum is going in anyway. Conveniently, this frequency is independent of the amplitude (i.e. how high the pendulum is swinging) and only depends on properties of the system itself.¹ This is called the natural frequency or resonant frequency of the system (there are nuances between these terms that don't matter in this context). So pushing at that frequency will lead to resonance and (without damping) the pendulum will swing higher and higher (its amplitude will become arbitrarily large).

The same is true for larger and more complicated systems, though they will ususally have multiple resonance frequencies.

_{1. This is strictly only true for harmonic oscillators, i.e. systems where the restoring force is proportional to the displacement; for a hanging pendulum this is only true for small angles, but for the sake of simplicity we'll ignore that in the context of this answer.}