The story: In this game you played not as Sir/King Graham (the protagonist of the first 2 in the series) but as Gwydion, the slave of the evil wizard Mannanan. To cut a long story short, Gwydion is in fact none other than Prince Alexander, son of King Graham and Queen Valanice (the later rescued by Graham in King's Quest 2 which I haven't played), who must somehow return to Daventry and free the royal family from the clutches of a dragon. To this end you had to master powerful magic that allowed you to do all sorts of magical things such as transform into animals, cause storms, understand creatures and become invisible.
King's Quest 3 was better than the previous 2 games for a number of reasons. For starters it was a much bigger game. The graphics improved a notch and supposedly it was one of the first games to have a cutscene (of sorts). The story was also more involving than the get-the-treasure (King's Quest 1) or get-the-damsel (King's Quest 2) storylines. You began as a young man, not knowing who you were and through the course of the game discovered your identity.
The game retained the standard text command system of the series (it wasn't until King's Quest 5 that this was dropped in favour of the mouse) and the type of graphics used (though this was improved a bit over the previous 2 games as mentioned earlier). The game was also much harder than previously seen in the series, with a time limit being used in the earlier part of the game as Gwydion tried to run around the countryside collecting items to aid him in the use of magic whilst Mannanan was away (items that could be used in spells were marked with an '*' in your inventory and you could potentially lose the game if Mannanan caught you with anything remotely magical). Of course like all the King's Quest games of this time there was a heavy reliance on puzzles inspired by classic fairy tales (check out The 3 Bears from Goldilocks). You were also able to cast spells whenever you felt like it (once you had the right ingredients), sometimes with amusing results - try casting a storm whilst on the pirate ship!
In the end it was a highly entertaining game, and probably ranks as my second-favourite King's Quest game (after King's Quest 5). Worth a good look.