In order to create suxh a function you fill up memory with results of some computation and then it later reads these values to further rhe computation. Rather then save the values, one could theoretically recalculate them when needed. So the memory is not really a hard requirement, but we build functions that without memorization require much more computatuon. Hence the time memory tradeoff.

In order to create such a function you fill up memory with results of some computation; the memory-hard function then reads these values to further the computation later on. 

Rather than saving the values, one could theoretically re-calculate them when needed. So the memory is not really a hard requirement. The memory hard functions are however build in such a way that they require much more computation without memorization of the intermediate values. This is the time / memory trade off.