As far as I have figured out, the stars represent which statistics are being increased by the '+' of the item (as well as being somewhat of a relic from earlier beta versions).

Each star represents a +5% to the associated stat. Hence 2 stars is +10% and 3 stars is +15%. Note that this does not affect stats "below the line", such as strength on a garnet ring.

Also note that any fractional result is always BUMPED UP to the next integer.

For example, take a ring with 3 defense.
ring+1 : 3*1.05 = 3.15 -> 4 defense
ring+2 : 3*1.10 = 3.30 -> 4 defense
ring+3 : 3*1.15 = 3.45 -> 4 defense

The moral of the story is ... HQ is not terribly useful on jewelry.