The Advance Ring is a Seed Ring that Link can purchase in the Advance Shop from Oracle of Seasons and Oracle of Ages. Link can only access the Advance Shop if the game is played on a Game Boy Advance. If Link is playing using a Game Boy Color, the shop is not accessible and Link cannot acquire this ring.
The ring is no different than any other Seed Ring, but when Link brings it up to the counter, the store owner, Stockwell, refers to the ring as the Advance Ring. If Link takes the ring over to Vasu at Vasu Jewelers, he can get it appraised. If Link purchased the ring in Oracle of Seasons it will appraise to the GBA Nature Ring. If appraised in Oracle of Ages is will appraise to the GBA Time Ring.
Both the GBA Nature and Time Ring have no effect at all. The sole purpose of these rings is an extra bonus for players who are playing on the Game Boy Advance console.