Random Properties are bonus modifiers found on most crafting recipes.
These are what they sound like; random modifiers, prefixes and suffixes that spawn on a given item and add to its stats.
Random properties are what keeps crafting interesting, mysterious, and unpredictable in Diablo III. You never know quite what you'll get, which turns item crafting into a bit of a gamble. This follows in the footsteps of crafting in Diablo 2, but it's very unlike the predictable, guaranteed outcome of item crafting in most RPGs.
Craftable item, with 2 random properties.