Wheel alignment is also called tracking. It is adjustment of various angles of the wheels to that of the manufacturer's specification to make the vehicle to track straight when not steered and to give the vehicle a good handling.
A good alignment helps a vehicle to track straight and steer easily. Vehicle handling characteristics is also improved with good alignment. Alignment is done by adjusting various wheel angles to specifications given by the manufacturer. These angles are carefully selected for good handling, performance, longevity of suspension parts and safety.
The angles that are often adjusted during alignment are toe and camber. Another one is caster. A well configured wheel will not allow the wheels to work against each other. We are trying to explain this in layman's perspective as much as we can so that it can be easily understood. Imagine that when the steering is at the center, the front left wheel is turned left and the front right wheel is turned right or vice versa, they are going to work against each other.
Now, how does this affect fuel consumption? The power that moves a vehicle is generated by the engine. The engine converts the chemical energy in the fuel to mechanical energy. When the wheels are working against each other, more power will be required to move the vehicle. This in turn implies that more fuel is going to be burned by the engine to generate the extra power.
In conclusion, let's use the analogy of a cart. If you are pushing a cart with wheels that are not pointing straight, you are going to expend more energy to overcome the resistance from the wheels.