Resonance happens in driven oscillators, where the frequency of the driving function is close to the characteristic frequency of the oscillator. In a tunable radio circuit, you change the characteristic frequency of the oscillator (the circuit) against a background of EM radiation (the driving function) - we do this because radio stations strongly transmit in narrow ranges. If you plot the strength of the resulting signal against frequency you get that up-down pattern, with a peak everywhere there is a radio station.
There are other ways this can happen - for instance, we can supply a driving field to some structure in nature. The structure may respond resonantly to the field - for instance:
Resonant tunnelling is a QM phenomenon where a particle can escape a confining potential despite not having enough energy to "go over the wall".
... the vertical axis is the
transmission coefficient and the horizontal is the energy (and thus the frequency) of the wave... as you'd expect, the higher the particle energy, the more likely it will get through the wall, so you get a general upward trend there. However, there are a bunch of sharp peaks appearing in the graph. These are the resonances. I count 7 of them.
... A resonance occurs where the width of the barrier is close to a half-integer multiple of the wavelength of the particle's wavefunction. It's like waves on a string - the resonances are the
harmonics.
You can also get absorption resonances that appear as troughs instead of peaks.
Resonance is characterized by a strong narrow-bandwidth reaction to an applied field.