There have been "minions" in the previous editions of D&D. In 1st and 2nd ed adventure modules there were often hordes of low HD humanoids in encounters, hanging around essentially as flavour. Both stats and combat options were limited, battlemaps often weren't used, and the game was able to cope with the numbers, more or less.
While AC and damage didn't ramp up as quickly as in 3e, nethertheless the average PC party would become immune to 1 HD orcs and their ilk fairly quickly (barring wussier magic-users who could keel over if coughed on even at appreciable levels). Typically they would die to fireballs or other area damage (whether they saved or not) or make the melee types "waste" a single attack to kill each one. Hell, area damage was good in 1e and 2e because of the wussy creatures that would die in droves to such attacks, which gave a psychological payoff to the player of the wizard even if the creatures were mostly harmless.
3e massively increased the amount of stats for monsters, and upped both hp and damage. This increased the DM workload, and significantly decreased the number of monsters a DM could efficiently run in the average encounter. Also, the spread of AC and damage over levels increased as well, so that monsters became obsolete quicker. Lower numbers of encounters with a smaller number of tougher creatures became the order of the day, and the disposable hordes all but disappeared. The general increase in HP without a corresponding increase in spell direct damage made blasting a lot less appealing.
The problem with minions in D&D so far is they were generally lower level monsters that weren't a direct threat to the PCs. For the DM it could feel it was wasted time running them, rolling buckets of dice in the hope of a 20, and them dying automatically to any area damage.
To me it looks like the 4e designers came up with some desired characteristics for 4e minions to make them easy to run for the average campaign - low book-keeping overhead, represent a small but credible threat to the PCs, easy to kill but not too easy.
So orc minions have appropriate AC, attack values and (fixed) damage for their level, but 1 hp so they are killed by any successful PC attack. However, they are immune to auto damage, again to make them a small but credible threat. Otherwise PCs would just focus on the non-minions and use autohit and splash damage on the minions - cleave etc.
Their availability makes it possible to raise the average number of opponents in an encounter without overwhelming the DM. It also makes area damage once again useful - while it won't autokill minions, it's still the most efficient way of dealing with them. Dealing with minions is what the controller is best at and what makes him look good. The other classes with single-target effects then won't waste their better attacks on mere minions.
The existence of minions may changes 4e tactics from previous editions. Novaing the best powers first in encounters, often practical in 3e, may be wasted on minions in 4e encounters, leading to problems when subsequent waves of reinforcements with the true opposition arrive. With the increased HP buffer, it may be better tactics to use at-will or encounter powers initially, resorting to dailys only when you know they are worthwhile.
And again, the minion rules are another step in separating PCs from NPCs/monsters rules-wise. The exact same monster may have different stats when encountered at different levels. The tough orc representing a significant challenge to the PCs when encountered first, may be represented as a mere minion in an encounter a few levels later.