Thne reason quasars are important to us is that due to the fact that they are some of the brightest objects in the universe - they can be seen from very very far away. This gives us insight into what is happening at the very farthest edges of our observable universe.
Light from distant quasars is hugely red-shifted. This red-shift is interpreted as rapid recession. In fact, it's pretty consistent that, the farther away an object is, the faster it is receding.