I am a relatively new player of D&D, having started with the 5e playtest and gone on from there. I have not played any on 1st to 4th edition. I have noticed quite a few threads on Warlords and have stayed away since so many threads seem like just an argument rather than a discussion. But now that it appears to have cooled down a bit I should ask, "What is a Warlord?"
The Warlord was a D&D class introduced in 4e*. It is a 'martial' class - that is, it doesn't cast spells or have supernatural powers - that models a range of heroic fantasy archetypes, mostly those having something to do with leading warriors in battle. The class included personal basic competence in melee that was merely adequate, the ability to Inspire allies to gain a variety of benefits (restored hps, temp hps, bonuses and 'buffs' of various sorts) and/or tactical planning or brilliance (modeled by allowing allies to move, attack, or take other specific actions out of turn, granting various bonuses, or even by tricking or maneuvering enemies into tactically disadvantageous positions) and specific combat maneuvers with dramatic effects (usually including inspirational or tactical benefits for allies) - among other bits and pieces. Ultimately the class had half a dozen or so 'builds' (like 5e archetypes), covering different variations on the concept from fierce lead-from-the-front Bravuras who gave their allies benefits when adopting aggressive tactics, to Tatics or Inspiration focued builds, to the opportunistic Resourceful build, all the way to the odd 'lazy' build that focused on giving it's actions out to allies (which could be used to model less warrior-oriented concepts like the non-combatant tactician, or the side-kick character whose presence and awe-struck faith in his heroes inspires them to even greater acts of heroism).
I'm looking for:
a basic overview of the class
specifics of what make the class unique
mechanics that reflect those specifics
That could get very, very long. The warlord had, as I said, multiple builds, each centering around a version of 'Commanding Presence,' that gave allies a specific benefit when they used an Action Point (a 4e mechanic similar to the 5e fighter's Action Surge, but available to all characters). The also had an Inspiring Word feature that triggered an ally's Healing Surge (which was comparable to rolling 1/4 of your HD or to the fighter's Second Wind), and granted an initiative bonus to allies. On top of those basic features, the warlord started with 4 maneuvers, two at-will the one 1/short rest (and short rests were a lot shorter, so essentially 1/encounter) one 1/long rests. Those latter two powers eventually increased to 4 each, plus 6 utiities over 30 levels. That matched the availability and power of spells that casters could cast, though, of course, maneuvers were much more limited in the range of effects they could have (no tossing lightning bolts or anything). Anyway, those maneuvers were chosen from a list of 3-6 at each decision point in the PH, expanding to a dozen or so, and among 30 levels of such choices, ultimately totaling 334 unique maneuvers, all together - again, comparable to the choices available to most PH classes, though well behind the Wizard and Fighter.
In 5e, casters have vastly expanded spell capability, starting with 3 dailies and going up from there, and having tremendous flexibility in what spells they prepare each day and cast each round (in 4e, spells & maneuvers were chosen at character creation and when you leveled up, only).
Obviously, the 4e model of the Warlord couldn't work in 5e, it would be wildly under-powered and under-versatile compared to the caster classes that make similar contributions to the party (the Cleric, Druid, Bard & Paladin, mainly).
And, if you feel one way or the other, why can or can't this be represented by what is currently present?
5e currently gives you a lot of ways to do any given character concept. If you want to play 'holy warrior,' for instance, you could play a Cleric and be a modest melee type, but a very good healer & buffer, with a fair amount of blasty and control magic, as well, focusing more on one than the other, depending on what spells you prepped that day and how you used your slots each round - you could choose the War Domain at 2nd level to be a little better in melee. You could also play a Paladin, with more emphasis on combat ability, but fewer spells. You could also play a fighter, take the Acolyte Background and at 4th level choose a feat that gave you a cleric-list spell or two (IIRC). You'll be very much a warrior, but you'll have very little mechanical support for being 'holy.' You could also just play a fighter and RP him as very pious. Obviously, Cleric is a great support class, the Paladin still a pretty fair one, and a mere Acolyte with a feat pretty poor, while the merely-RP'd-as-pious fighter is no better at support than any random PC or NPC.
Currently, you could build a 'warrior who leads other warriors in battle.' You'd take the Soldier Background for Rank or Noble Background for status, choose Fighter, at 3rd, choose the Battlemaster Archetype and 3 of the 4 maneuvers it offers that are a bit like some of the 334 maneuvers that the Warlord had (Rally - temp hps; Comander's strike - attack-grant that is rarely as good as just attacking yourself; maneuvering attack - one ally can move 1/2 speed; and Distractig strike - advantage for the next ally's attack) , and at 4th level, take the Inspiring Leader feat, allowing you to grant temp hps. Like the Accolyte Fighter with Magic Initiate (Cleric), you are expressing the concept, just in cursory way with little mechanical support, that isn't an adequate substitute for the support functions provided by the real thing.
* Since you're new to the game with 5e, you may not be aware of the controversy surrounding the introduction of the last edition, in 2008, which for various reasons (it was 'too soon' after the last rev-roll in 2000, WotC was disrespectful to fans in it's releases, the rules changed too much, 'martial' and caster-classes were more nearly balanced than ever before, etc) sparked an acrimonious internet storm of nerdrage we call 'the edition war.' Since the Warlord was introduced in the first 4e book, the Players Handbook 1, while all the classes in 5e, so far, had their origins in even earlier editions, there is a great deal of lingering hostility towards the Warlord, specifically.
5e was conceived, in part, as a new edition to bring fans of all prior editions together after the craziness and animosity of the edition war. So far, it has done an excellent job of evoking the feel of AD&D (1e & 2e) with the vast majority of the game calling back to that classic period, and has significant, optional mechanics (feats and multi-classing), as well as two classes (Sorcerer & Warlock) that were originally introduced in 3e, as well as minor mechanics, often under different names and with different spins, taken from both 3e & 4e, and the significant overnight healing and up-from-zero healing mechanics that were taken from 4e.
What it lacks is a class that was introduced in 4e, like the Warlord, which was a PH1 class, and very well-supported in subsequent materials.