What does "absence makes the heart grow fonder" mean?

Separation intensifies love, as in After a year in another country she accepted his proposal, so I guess absence makes the heart grow fonder, or, used ironically, The boss leaves earlier every day; oh well, absence makes the heart grow fonder. Although versions of this saying date from Roman times, it only became popular after Thomas Haynes Bayly used it as the last line of a song in The Isle of Beauty (1850). The opposite sentiment is expressed by familiarity breeds contempt.