Question

why is the doppler effect important

Answer 1

If you understand the basics of doppler effect, it have its uses too, like in radars and identifying velocities of various objects

Answer 2

It is important because firstly it is cool and physicists like cool things. Secondly, because of its usefulness. In everyday life, it is used to check if vehicles are over speeding and in some sports. But the interesting part is that it formed the basis of our current understanding of the Universe.

There's a thing called Hubble's Law which states that the farther a galaxy is from us, the faster it recedes away. OR v = Hd where v is the recession velocity, d is the galaxy's present distance to us and H is Hubble's constant. Edwin Hubble measured the redshift or rather the difference in redshifts of different galaxies. So, in this way the modern picture of the Universe came about through the use of Doppler Effect. you can check it's equation on Wikipedia.