A phrase meaning "what he or she deserved." For example:
"Sooner or later they'll catch that murderer Crazy Jim McNutcase, and then he'll get his just deserts."
Note that 'deserts' is not spelled with a double 's'. This phrase is often incorrectly spelled as "just desserts." It's an easy mistake to make, because it's pronounced with the stress on the second syllable, just like 'dessert'. Most people are familiar with desert meaning a large sandy place and dessert meaning a sugary dish, but this is another word altogether, from the French 'deservir', meaning 'deserves'.
See Webby's entry under desert, you sceptics :-)