From Diablo Wiki
Cooldown is the time it takes from casting a spell or drinking a potion until a new spell can be cast, or a new potion consumed. Diablo III uses cooldowns extensively, and abilities or skills on a cooldown show with a greyed out icon, while a second hand moves around the inside of the icon, changing the color back to show how long the cooldown has remaining.
Cooldowns are used in Diablo III to limit the power or frequency of abilities or actions. Health potions have lengthy cooldowns between uses, and many powerful skills have cooldowns as well. These times may be modified (generally reduced) by skill runes or other factors.
Cool downs are used by the developers to add a level of strategy and variety to skills, as well as to limit the power of very high level and powerful skills. Cool downs do more than just resource costs, plus they allow characters to continue fighting and using other skills; just not the big one with the cooldown on it.
 Cooldown versus Cast Time
Sometimes spells or abilities have a long cooldown because they have a short cast time. These two are often balanced against each other. The advantage of a long cooldown over a long cast time is that a player can still run around and use other spells while waiting for the powerful more spell's cooldown to run out.
 Lengthy Diablo 3 Skill Cooldowns Revealed
This information was offered without explanation or context, and set off huge fan debates. While some players disliked the concept of long cooldowns in a Diablo-style fast action click-fest, a lot of players, especially those who have grown used to multi-minute cooldowns in games like World of Warcraft and Rift were not upset by the concept coming to Diablo III. Bashiok added some explanation a few days later, repeating many of the arguments fans had been offering since the initial word hit.
For instance Call of the Ancients literally calls down the four barbarian ancients to fight alongside you. How would that work if it was spammable? Should we make it cost 100% resource to keep you from being able to spam it, and then leave you drained to Cleave back enough Fury to follow it up with anything? That doesn’t sound like something *I* would take. Maybe someone could find a build for it, I don’t know.
Bottom line is that cooldowns allow for skill complexity or power by limiting them in a meaningful way because it can mean long-term balance even as stats inflate. We do want to make sure we’re only using them where appropriate, though.
Most fans seemed to accept these arguments, and others in favor of the system, as demonstrated by a vote run by Diablo.IncGamers.com on the issue. As of July 19th, nearly 60% of voters either loved or liked the system, while 35% disliked or hated it.
 PvP Ramifications
The issue of long cooldowns on skills comes to the front in terms of the Battle Arena, where the PvP is very fast and hard-hitting and most rounds are less than a minute long. Obviously, a skill with a two-minute cooldown wouldn't be used very much in such a PvP encounter, but by its very rarity comes its power.
Players will have to wait until just the right moment to use their biggest skills, since they'll only get one use in most rounds. Landing a good hit with such a skill should be a game-changer, but missing with it would be devastating. And all the while the opponent(s) would be waiting for just the right moment to spring their nuke-skill or skills. How these single use, mega-skills will work into arena strategies, compared to lower level skills that can be spammed all during the round, will be an interesting process to observe.
 Global Cooldown
Some games also use a mechanic called a "global cooldown", which will affect all spells, skills and items. It's a measure making it easier to balance the game, limiting the number of things a player can do at once. All skills are not necessarily affected by global cooldown, or trigger a global cooldown. There is no such feature in Diablo III.
Cooldowns were originally set primarily on CPU/GPU intensive graphic effects that could cause lag in multiplayer games when a player spams that spell.