[FIXME: This chapter is based on Mikael Djurfeldt's answer to a question by Michael Livshin. Any mistakes are not theirs, of course. ]
Weak references let you attach bookkeeping information to data so that the additional information automatically disappears when the original data is no longer in use and gets garbage collected. In a weak key hash, the hash entry for that key disappears as soon as the key is no longer referenced from anywhere else. For weak value hashes, the same happens as soon as the value is no longer in use. Entries in a doubly weak hash disappear when either the key or the value are not used anywhere else anymore.
Object properties offer the same kind of functionality as weak key hashes in many situations. (see Object Properties)
Here's an example (a little bit strained perhaps, but one of the examples is actually used in Guile):
Assume that you're implementing a debugging system where you want to associate information about filename and position of source code expressions with the expressions themselves.
Hashtables can be used for that, but if you use ordinary hash tables it will be impossible for the scheme interpreter to "forget" old source when, for example, a file is reloaded.
To implement the mapping from source code expressions to positional information it is necessary to use weak-key tables since we don't want the expressions to be remembered just because they are in our table.
To implement a mapping from source file line numbers to source code expressions you would use a weak-value table.
To implement a mapping from source code expressions to the procedures they constitute a doubly-weak table has to be used.