That pun is intended to incite interest in what promises to be a not so interesting subject. The new D&D 5e has been built along a line of balance reminiscent more of the OD&D era than the modern era, but the use of a decidedly MMO term like tiers might make it seem otherwise at first glance.
Previous editions of D&D did not discuss tiers of play. Levels told the players and DM what sort of threats were appropriate. Whether those threats were monsters, dungeons, or modules, the levels acted as a guide. Indeed the Basic edition (1981) lays out that the level of the monster should match the level of the dungeon such that a weaker (lower level/hit die) monster, when found on a deeper (higher numerical level) level of a dungeon would be found in larger numbers to account for the increased threat. In that same edition the classes (fighter, magic user, cleric, & thief) shared the same "to hit" value for their first 3 levels. At level 4 the fighter advanced by 2 points followed by the cleric at level 5 and the magic-user at level 6. In a way the tiers were already present but nobody was calling them tiers.
MMOs call things tiers. An MMO might group its levels into bands of levels all of which have a similar success rate and chance of survival as determined by the game developers. Let us say that an MMO has 50 levels. The developers might determine that levels 1-10 were Tier 1, levels 11-20 were Tier 2, levels 12-30 Tier 3, levels 31-40 Tier 4 and 41-50 Tier 5 (also called Endgame). The argument would then be made that every character in a Tier was on relatively equal footing. It's not true in a micro sense, of course, as hit points and hit bonuses can vary wildly, along with powers and abilities, but in the macro sense the threats in the Tier 1 zone will be matched to be a challenge for those levels. Once the player's character moves to the next tier the threats of Tier 1 zone are no longer a challenge. If a Tier 1 character enters the Tier 2 zone certain death awaits. That's the MMO way.
Tabletop has always been, basically, the same as the MMO concept, except with more freedom to exploit those tiers. A group of 1st level characters typically know better than to go hunting an ancient wyrm red dragon. Good DMs know better than to force their Tier 1 players into going after an ancient wyrm red dragon. The tiers have always been there, people just weren't calling them tiers of play.
The new D&D 5e has a section in the Player's Handbook that expressly defines the tiers of play. Levels 1-4 are the apprentice tier where the characters are being defined, learning the ropes and finding their footing in the world. Levels 5-10 represent the second tier where the characters "come into their own" in terms of who they are. Spellcasters start to get those cool spells like Fireball that really tip the balance in the clinch situations. Levels 11-16 are the third tier where the player characters are actually a cut above regular adventurers. They've made names for themselves and to ordinary people they are legends. The final tier, levels 17-20, a mere 4 levels are the truly legendary levels. The players are now movers and shakers on a cosmic scale. Scale; it's all about scale.
Which is what makes this system work.
Starting around the time of AD&D 1e a considerable and ever-widening gulf appeared between the classes with the two extremes being the Fighter on the physical end and the Magic-User on the mental end. By the time of 3e the "to hit" potential in melee combat, not to mention hit points, of the Fighter was so far beyond the Mage that a Mage had no hope should his spells run out. You could, with careful feat selection find a way to give your Mage a fighting chance against a goblin with a gammy leg, but otherwise he'd best stay far away from melee. In the 5e rules every class has the exact same base bonus to hit: the proficiency score. That score starts at +2 for 1st level and increases at 4 level intervals by +1 until finally arriving at +6 at level 17-20. Thus a Fighter with no strength bonus (I know, it wouldn't happen) and a Wizard with no strength bonus (far more likely) each holding a dagger (both classes are proficient with daggers) both have +6 to hit. Yes the Fighter likely has far more hit points and better AC, so the melee advantage is to the Fighter, but the gulf is not so immeasurably wide as it has been in the past. It looks a lot more like OD&D in that respect, which is probably a good thing. The theory of adventure design, much like dungeon design, says to start simple and work toward the epic. Let the party cut their teeth on kobolds and goblins, then lead them to the bigger challenges before baiting the epic quest hook. Let's face it, the DM's job is hard enough as it is, the Tier system is a useful tool to help the DM scale the appropriate threats for a challenging, but rewarding adventure.