Tarot cards give buffs or stats boosts when applied to your hero. Having two or more of the same symbol (card) gives more of a stat boost. Having all 4 of the same card unlocks a bonus buff/stat boost.
The different colour of the cards tell you how good the buff or stat boost will be. Green being the lowest, Orange the highest.
You can't use the fate crystals yet as the devs haven't added that part in yet.