Nuking the fridge is simply the act of creating more storage space in your cold storage unit, and/or saving money; by eating all the leftovers which are starting to get... bigger.
In many locations, heating something in a microwave is called 'nuking' it - due to a poor
understanding of the structure of the
electromagnetic spectrum.
Similarly in many locations the word
refrigerator is shorted to 'fridge'.
Thus from the combination, we get 'nuke the fridge' - to heat up chilled leftovers from your fridge, in a microwave. It's not complicated, not should it be.