Why is the neutral very imprtant and where is it used?

Neutral is the center point between two designated supply taps, T1 and T2.

For example, if the Voltage supply between (N) and (T1) is 120 VAC, and we know point (N) is the zero point between the equidistant points of (T1) and (T2) we can conclude that the Vac between (T2) and (N) is electrically speaking 120 VAC.

Now remove neutral. You now have 240 VAC across (T1) and (T2). Every single circuit inside your house will carry 240 VAC across it.

Pack your bags, get into the car and chase the house until to can cut the power off. By the way, anything connected to internal branch circuits is probably toast of the very crisp or melted, but relax the resulting fire will reduce clean up time

Any one ever tells you that you don't need a neutral line, have him arrested and shot dead on the spot for the crime of <you pick it>