While efficiency refers to how well something is done, effectiveness refers to how useful something is. For example, a car is a very effective form of transportation, able to move people across long distances, to specific places, but a car may not trasport people efficiently because of how it uses fuel.
edit Using Effectiveness and Efficiency
Effectiveness is about doing or using the right things — things that yield positive results. Efficiency is simply about doing things right — i.e., completing a task cheaper or faster.
Ideally, individuals and companies find ways to be effective and efficient, but it is possible to be effective, but not efficient, or vice versa, or neither. For example, if a company is not doing well it may decide to train its workforce to use a new technology. The training may go well, with employees learning the new technology in record time, but if overall productivity doesn't improve following the implementation of this new technology, the company's strategy was efficient but not effective.
In the following video, William McDonough, co-author of The Upcycle: Beyond Sustainability--Designing for Abundance, speaks about efficiency vs. effectiveness: