Points are the currency for MGs.
Mika has posted a spreadsheet with a lot of information about points: Points Madness.
They are gotten by quests, killing anathema, and saving people. Only the person who makes the killing blow gets points for killing anathema, unless they are in a party. If they are in a party, points are shared among party members; I assume evenly.
The points one gets from killing anathema depend only on the type of anathema – its level and the MG's level do not affect how many points you get.
The points one gets from quests is affected by your level: [Every hundredth level you achieve will increase the amount of possible points that can be rewarded to you through quests.] Selene, ch. 30
Points can be spent on Permissions (Vaults and Grimoires) and Skills. Skills must be unlocked before they can be bought; Common permissions just take points. Higher tier permissions may be bought once one reaches the appropriate level – every hundredth level opens a new tier. Once a permission has been bought, an MG can buy items from vaults, using the Arcane Gate system, and spells from grimoires.