Experience or EXP cards for short are the essential material required to level your servants as they do not get any EXP for themselves by completing battles, only Bond Points. Levelling your servants is a very important aspect in the game as it increases their base HP and attack, which are necessary if you want to complete the harder stages within the game.
There are eight type of EXP cards in the game currently, one for each of the seven main classes and the eighth type is for every class. Feeding the same EXP card to servants of the same class will give a bonus of around 1.3x experience (27,000 > 32,400 EXP), so if you have quite a few Extra classes servants such as Ruler or Avenger, you might want to save some of your all classes EXP cards for them as they do not get the bonus from the seven main classes EXP cards.
EXP cards are classified from 1 star to 4 stars but generally you would only be feeding the 4 stars EXP cards to your servants as it provides triple the experience compared to the 3 stars ones, making it the more QP efficient way to level your servants.
3★ cards for Mana Prism
3★ cards can be traded for Mana Prism at Da Vinci Workshop. Tap "Burning (Sell)" button to convert 3★ cards into Mana Prism. Mana Prism can be exchanged for Summoning Ticket.
How to get
The most effective way to gather those 4 stars EXP is by running the 40AP daily quests in the Chaldea gate. The type of EXP cards obtainable from the daily quests differ from day to day, which are shown as follow: