Devotion is a mechanic introduced in Theros, where it was connected to the god theme of the set. It always appears as Devotion to [color], where color is either white, blue, black, red or green. Devotion to a color is defined as a numerical value that a player has, equal to the number of mana symbols of that color in the mana costs of permanents he controls. There are cards that count devotion to each of the five colors, and they have many different effects based on that devotion. 
Devotion is a mechanically retweaked version of chroma with a new name and flavor. 
From the Comprehensive Rules:
- 700.5. A player's devotion to [color] is equal to the number of mana symbols of that color among the mana costs of permanents that player controls.
- Numeric mana symbols (, , and so on) in mana costs of permanents you control don't count toward your devotion to any color.
- Devotion counts only mana symbols in your permanents' mana costs — the cost in the upper right corner of the card.
- Mana symbols in text boxes of permanents you control, such as activation costs or the big mana symbols on basic lands, do not count toward your devotion to any color.
- Only colored mana symbols count; it doesn't matter how much a permanent costs to cast, just how much colored mana.
- If an activated ability or triggered ability has an effect that depends on your devotion to a color, you count the number of mana symbols of that color among the mana costs of permanents you control as the ability resolves. The permanent with that ability will be counted if it's still on the battlefield at that time.
- Hybrid mana symbols, monocolored hybrid mana symbols, and Phyrexian mana symbols do count toward your devotion to their color(s).
- A permanent that costs adds one to your devotion to black.
- A permanent that costs adds three to your devotion to red.
- A permanent that costs adds one to your devotion to green and one to your devotion to white.
- A permanent that costs adds two to your devotion to red and two to your devotion to green.
- Gray Merchant of Asphodel -
Creature — Zombie
When Gray Merchant of Asphodel enters the battlefield, each opponent loses X life, where X is your devotion to black. You gain life equal to the life lost this way. (Each in the mana costs of permanents you control counts towards your devotion to black.)
There is a total of 16 cards that involve devotion, which divide by color as such:
- Black = 31 %
- Green = 25 %
- White = 12 %
- Blue = 12 %
- Red = 12 %
- Land = 6 %