I'm going to quote another italki member here. A while ago, someone on this site wrote a perfect illustration of the difference between these two words. Imagine cleaning the floor of your house with a small toothbrush. Cleaning the floor with a toothbrush is effective, because it will get your floor nice and clean. However, cleaning your floor with a toothbrush is not efficient, because it would take an enormous amount of time and energy to do it. That is the difference. It's a nice example, isn't it? I can't remember who it was who came up with it, but if they happen to read this - Thank you!

If something (or someone) is "effective", it works and produces the intended effect. If something (or someone) is "efficient", it works in an economical manner, using resources well. e.g. My car is very effective at getting me to work every day. I would be in trouble without it. e.g. My car is very efficient in its use of petrol (US "gas"), and so I save a lot of money.