Color balance
The color balance of a deck refers to the interaction of two parts of that deck. The first part is the deck's mana sources and their colors. The second part is the deck's mana costs and their colors.
Color slots
Color slots refer to a technique that evaluates how much of a deck's mana base is required to support a color on a given turn. The technique is best explained by examples.
For now, let us consider a deck using a basic curve, as referred to in "Mana curve", and only basic land.
Let us start with "60 cards, play first". In these decks, we have 24 land. The first turn color slot requires at least 9 land. The second turn slot requires at least 8 land, third requires 7. Conveniently adding up to 24 land. Hence, this deck could be three colors provided that no spell required more than one of any particular color of mana and that all one-drops were color 1 and all two drops were either color 1, color 2, or both. Three and four drops are free to be any of the colors or combinations there of provided they don't break the 'only one of a given color' rule. This may be notated by C1/C2/C3. For future calculations a final fourth slot would open on turn four if there were space for 6 land of that color.
If this deck wanted to us double colored mana costs then it would have to dedicate 15 land to support the cost on turn two, 13 to support on turn 3, or 12 to support it on turn 4. Clearly, doing so absorbs two of the decks color slots. So this deck will be confined to two colors, denoted C1/C2/C1 even though this would support double mana spells on turn two and leave space for colorless land.
For triple cost or above this gets even more restrictive. Triple cost on turn three would require 20 land, or turn four would require 18. The first case restricts us to a monocolored deck when we are only using basic land, C1/C1/C1. The second opens up the elusive fourth color slot, C1/C1/C1/C2, i.e. a splash.
Reverse Mana Syndrome
Some cards can be so powerfull in a deck that players can actually "reverse" the normal way that the colors are repressented with lands. If for example a black card is powerfull enough to win the game as soon as it is played (or soon after) it will be crucial to have that mana. If the deck has 36 red spells and 4 of these black spells it can be necessary to play with 8 mountains and 16 swamps. Players rarely use this syndrome, even though it is vital in a few odd decktypes.
(Further examples in the future)