'Effective' means that it does what it is meant to do.
'Efficient' means that it does this while making good use of resources - for example, not wasting time, energy, manpower, fuel or money.
A while ago another member came up with a really nice example which I'll quote, once again. Imagine that you clean all the floors in your house with a tiny toothbrush. This is an effective method, in that it will get your floors very clean. But it is obviously not an efficient method, because it will take a very long time, tire you out and wear out a lot of toothbrushes. With thanks to the originator of that illustration.