When you find sets in dungeons/trials they are not bound immediately. You can trade them with your group members for 2 hours (even after leaving group and the dungeon). After 2 hours they are automatically bound to you. Equipping them before makes them bound and no longer tradable. You can also manually bind them by right click and select bind. Make sure you bind them before selling to npc vendor or destroying them. You cant sell them in guild traders or any players other thsn who you were grouped.
Once bound the item is added to the "sticker book". From there you can reconstruct the item as many times as you want but it costs transmute crystals and need access to transmute station.