Making a book-keeping stat into an incentive
Item levels were originally an internal number used to determine how many stats each item got. In principle, you could use this meta-stat (after accessing it via third party database or UI add-on) to compare gear (or to argue on the forums that a specific item should have higher stats based on its ilvl), but in practical terms it was irrelevant to players for years post-launch.
Ilvl shot to prominence midway through the Wrath of the Lich King era when players began using a third-party add-on called "Gearscore" to add up the ilvls of a player's gearset as a quick and dirty way to check whether the player's gear was plausible for the content your group intended to complete. Gearscore was not without controversy, but Blizzard brought it into the game's base UI anyway, adding the average ilvl of the player's gear to the UI and using it as a screening mechanism for the random group finder in patch 3.3.
This change happened comparatively late in that expansion cycle, and applied primarily to content that players were already routinely and trivially completing (easy 5-man heroic dungeons). Going out to get gear specifically to meet a minimum ilvl to be allowed into content came later, most prominently with the addition of the raid finder in Cataclysm's final patch. During the same window, we've seen each raid expand to three separate tiers of loot - differing primarily in ilvl and associated minor bump in stats - that only further emphasize that increasing ilvl is an incentive in its own right, and not just something that happened incidentally as you upgraded your gear.
Comment Update: Commenters point out that ilvl scaling is actually less linear than I remembered, making the upgrade system too powerful, not too weak. The rest of the reasoning in this post about why focusing on ilvl as an incentive is a bad idea stands (and actually makes more sense with the correction).
A Technical Increase In Power
The new item upgrade system in patch 5.1 crossed an important line - increasing the ilvl of gear (along with marginal bumps to its stats) was explicitly used as an incentive. The intent was to extend the benefits of continuing to earn valor points (from daily quests, random dungeons, etc) by allowing them to be used for small upgrades to certain gear. A bump of 8 ilvl's may sound significant until you consider the context.
In the launch game, ilvl's corresponded roughly to the level at which the player obtained the item. However, max level group content at each of the game's level caps led to dramatic inflation of item levels, such that gear at level 90 is approaching ilvl 400. As a result, the new system was only a 2% boost to the ilvl of one of your pieces of gear (out of 15-16 depending on whether you use a two-handed weapon).
Even if you did eventually get this bump across the board (I'm not familiar with whether every single slot could actually be upgraded this way), a 2% increase in ilvl for all of your gear does not directly lead to a 2% increase in DPS or other output. Other factors, including your inherent base statistics, scaling rules for increased combat ratings, and most importantly actual player performance are also going to impact character performance.
In short, this mechanic was technically an increase in character power, but functionally small enough that it's all-but cosmetic.
Running into the "optional" debate
Blizzard's defense of the item upgrade system hinged on two arguments. First, they state that players will quit if there is not stuff for them to do, and that many players will not do any in-game activity that does not increase their character power. I think we can agree that this is mostly sound reasoning, with the caveat that most players would really prefer that "stuff for them to do" take the form of new content on a more frequent basis, rather than incentives to run the old stuff into the ground.
Having said all of that, Blizzard tried to have it both ways by saying that the upgrades, while intended as an incentive to convince players to get valor points, are optional. This argument is sound from a game design perspective f
Players were already complaining that they felt daily quests were not optional because the resulting reputations are required to purchase entry level gear to start raiding. Allowing item upgrades exacerbated the situation because players eventually either run out of reputations to grind or else acquire superior gear by other means. I don't believe the system worked on all gear, but it worked on enough gear to make these players feel that they were now obligated to continue doing stuff they did not want to do in order to get valor points to pay for the upgrades.
I don't think Blizzard's position was wrong from a design perspective. However, as I wrote a few months ago, I think they lost this battle for the same reason that they lost the battle over dungeon difficulty early in Cataclysm.
Failure of the skinner box
Blizzard is still in the business of trying to sell a service to customers, and you can only get so far by telling a customer who is dissatisfied that the merits of your design trumps their preferences. If you tell the customer that they need ilvl - directly through minimum requirements for the raid finder and indirectly by using ilvl as an incentive - you should not be surprised that they believe they need ilvl. Once that has happened, it is natural for these customers react poorly when told that they have to do something they do not want to do in order to get the ilvl they think they need.
As Tobold points out in a post examining the motivations for botting, MMO's have increasingly misused incentives as a means of pushing players into trying other forms of gameplay - daily quests, dungeons, PVP, etc - that they do not enjoy. History has shown time and time again that this CAN change player behavior, but DOES NOT change player preferences. The numerous unsavory reactions - joining PVP matches only to try and sit AFK for the currency rewards, requiring gearscores far in excess of what content was designed for, and threatening to cancel because you feel "forced" to do daily dungeons - are a natural response.
I recognize that studios are struggling to produce enough material to keep people paying, and that they need to get each player to use as much content as possible. I recognize that incentives can be the difference between enough players in the dungeon queue to fill groups in a timely fashion and leaving newcomers high and dry. In the long term, though, reducing the game to a "Skinner box" activity that you do only because it is a prerequisite for something you actually want to do (e.g. raiding with your friends) is a recipe for burnout and churn. This particular example of pushing an arbitrary number far beyond its functional significance was an extreme case, but it is by no means the end of the issue.