To be effective means you are making progress to your goal. To be efficient is usually used in measuring how much of your resources are being used (like measuring fuel efficiency in your car... how kilometers can you travel on one liter of petrol?) or measuring a rate or speed.
For many people the words "efficiency" and "productivity" have the same meaning. To me there is a bit of a difference: Imagine a guy is great at cutting down trees and making wood for fires. He may be the most efficient person to ever hold an ax.
He is very efficient.
However, this woman using a chainsaw will be much more productive than him.
Productivity: Output per unit of input. It is one of the most important concepts in business/economics. Why? In the long run companies and countries that are able to create more productive workers will see their companies and countries grow faster.
Increasing productivity is one of the most important factors in the long-term growth of an economy.