Charms are one-time use items that give you a small boost for 1 hour.
Shiny Charm increases your shiny rate
Item Magnet Charm increases the chances of wild Pokemon holding items (Everstones, Heart Scales, etc)
Exp. Charm increases the amount of experience you gain
Riches Charm increases the amount of money you earn from PvE battles
Battle Points Charm increases the amount of battle points you earn from PvP & PvE
As Akshit mentioned, Shiny Charm is an increase of 10% while the others are all 25%. hope this helps