A really good example I found on Wikipedia of all places:
If you had brain surgeons digging ditches, and they were all digging ditches to the best of their ability, and they could not possibly dig any more ditches than they are ditching without extra resources, then you have technical efficiency. This is because you are getting the maximum output from a given level of input (maximum ditches from a given level of brain surgeons).
However, brain surgeons digging ditches isn't what's best for society. If they stopped digging ditches and performed brain surgery, society would have fewer ditches, but more brain surgery. Assuming society places a higher value on brain surgery, than ditches, the total satisfaction society gains from its allocation of resources (that is, the decision to have brain surgeons doing brain surgery, rather than digging ditches) has increased, and there is greater satisfaction in society. Does that help to shed a little more light on it.
technical\productive efficiency =maximum output from given resources
allocative efficiency= best possible use of given resources in order to benefit society.