Dipole antenna resonance frequencies
When you don't match the antenna length to the frequency you are trying to radiate or receive (it happens a lot of times) you get a more complicated impedance presented to the electrical terminals of the antenna: -

It's the same for transmission lines; if the end of the t-line isn't matched in the characteristic impedance you get internal reflections that can make the feed-end of the t-line appear to have a higher or lower impedance depending on how long the t-line is in wavelengths.
Antennas still can work with a highly mismatched length but the resistive part of the impedance (that part of the impedance that represents the real power of the signal being transmitted into space) can be anywhere between a fraction of an ohm and several kohms, in series with a large reactive impedance. Crystal radio antennas are good examples of this because you will never likely make a monopole of a quarter wavelength because it'd be physically too long so, the reactance part plays a big role in electrical tuning when used with a coil.