The purpose of the badge system is to increase your 5 basic stats: Intellect, Spirit, Dexterity, Physique and Strength. The badges can be obtained through PvP and PvE dungeons. Level 1 badges can be obtained through the Level 1 Badge Chest. Higher level badges can be obtained by combining the lower level ones. You can buy the badge directly from the Order of Guardian Store (for Demonslayer Points) and the Military Store (for PvP Points) or buy the badge fragments.
Badges can be salvaged into fragments. These fragments need to be crafted into badges. Look for the NPC Jela Jora (1574, 1580, 183) to help craft these.
If you accidentally craft the wrong badge, you can salvage these badges into fragments without any loss and recraft the badge you wish.
Badges can also be augmented by attaching runes into them. Runes can also be salvaged into rune fragments. And rune fragments can be combined back into runes.