Impedance matching can actually be related to diffraction. When you see a beam of light enter water, the beam of light bends. You also get some reflection off the surface of the water. The reason for this is because of impedance matching.

Water has a different impedance than air or free space for electromagnetic waves. This abrupt transition in impedance causes some waves to be reflected off the surface and some to be transmitted (but simultaneously refracted at a different angle). The angle of refraction is directly related to the impedance which is also directly related to the speed of light in that medium (in this case water).

Now, if the impedance varies drastically between the two mediums, you sometimes get almost complete reflection. Such as case would be when light hits metal, it pretty much entirely reflects off.

In the case of an antenna, your incident waves or photons (electromagnetic waves are comprised of photons), are travelling along your signal cable feeding the antenna. The antenna itself, because it is different in shape and materials and many other things than the signal cable, presents itself as a different impedance than the cable. If this impedance is significantly different than that of the cable, you get mismatch, in which case most power is actually reflected inside the cable at the cable/antenna interface, and your antenna no longer radiates properly (very little power transmitted). If you match the antenna impedance perfectly to the cable (which is done through matching), you can make an almost seamless transition between cable and antenna where almost no power is reflected.

For a dipole antenna, when the dipole is near half a wavelength the impedance is around 70 Ohms, very similar to that of the 50 Ohm/75 Ohm cables we use to feed them. Thus dipole antennas are impedance matched. However if we change the length of the antenna to say 1 wavelength, the impedance can go up into the 1000s or 10000s or get crazy high, in which case you get a large impedance mismatch.