You may have heard the terms "redshift" and "blueshift," which refer the stretching and contracting, respectively, of waves. This works with any type of wave -- light, sound, water, etc.
But when astronomers talk about redshift or blueshift, we're almost always talking about light waves. Objects that emit light -- like stars or galaxies -- are constantly emitting light. When a source of light moves, it continues to emit light at the same rate (astronomers call this a frequency), but we receive the light at different times.
A redshifted source is moving away from us, and as it moves away, the lightwaves take longer and longer to reach us. The amount of redshift -- the amount that the lightwave gets stretched -- can tell us how fast the lightsource is moving.
Ambulance siren doppler effect was the first real world physics thing that blew my mind