Long story short, osmosis. Osmosis is the movement of a liquid solvent through a semi-permeable membrane from a lower concentration to a higher.

This means simply that when the yeast is in a very sugary (or salty, or one with any other solute for that matter) liquid, osmosis will cause it to lose water through its cell wall. As with all living organisms, yeast requires a certain amount of water within its cell to thrive and survive. Being in a very salty or sugary place will disrupt that careful balance by 'sucking out all of the water' and possibly killing the yeast.

This is actually used as a method of preserving food by inhibiting the microorgansims in the food. Both salted meat and jam use this method.