Both L sounds involve raising the tongue, but with the light L the tip of tongue approaches the alveolar ridge (the part of your gum just behind your top row of teeth), while with the dark L the tip of the tongue does the same thing, but the back of the tongue simultaneously rises towards the soft palate (this is called "velarization", and it's the same gesture that accompanies lip-rounding to form a W sound). There may be further differences depending on accent, e.g. in Cockney accents the tongue-tip gesture of dark L is lost completely so that dark L becomes a fully-fledged vowel, and it might even acquire lip-rounding and merge with W. Other accents have lost the distinction as well and generalized either light L or dark L to all positions (e.g. Scottish English tends to use dark L everywhere).
In the older pronunciation of "falcon", there's no L there at all, light or dark. It was borrowed from Old French "faucon", and the L was restored in spelling via Latin influence in more or less exactly the same way as the B in "debt".