A resource allocation scheme (usually for memory). Best Fit tries to determine the best place to put the new data. The definition of 'best' may differ between implementations, but one example might be to try and minimise the wasted space at the end of the block being allocated - i.e. use the smallest space which is big enough.
By minimising wasted space, more data can be allocated overall, at the expense of a more time-consuming allocation routine.
Compare First Fit.