Left hand Bracelets are for summoning Agathions, which are creatures that have various skills and also serve as decorations.
Right hand Bracelets are for using Talismans, which help with fighting monsters and other players.
Left hand Bracelets
Left hand Bracelets are used for summoning Agathions.
Equipping a left hand Bracelet unlocks Agathion slots.
The amount of slots depends on the Lv. of the Bracelet, there's always 1 main slot and from 1 to 4 of additional slots.
When an Agathion bracer is equipped, open the Skills Window (Alt+K or by pressing "Skills"), and you'll see the skills related to the Agathion in the active skills section (if the Agathion has any active skills).
Acquiring left hand Bracelets
There's only one kind of left hand Bracelets: Agathion Bracelet, which can be enhanced up to Lv. 5.