There are many good suggestions in this thread already, so there's not much I can add to it; but I'll try anyway.
I'm going to start by paraphrasing the suggestions of [MENTION=6696971]Manbearcat[/MENTION], because his is the best post so far:
The Warlord should lead from the front (or at least some Warlords should, though maybe not the lazy Warlords); influence the scope of battle; improve preparation for contingencies; instill hope; Heal morale damage; defend against fear effects; Improve the action economy; effect advantageous negotiation.
Generally, I think the Warlord should give the effect of improved tactics, though it might not be necessary to spell out how in each case: so, for example, the Warlord has ways to grant (combat) advantage, even if only once per encounter, but it might not be clear exactly what happens when he does so; or, for another example, the Warlord can insert allies into flanking position, though how he does it may not be clear; or he can extract allies from surrounded conditions, again with the means unclear; or he can augment the strength or effectiveness of an allied attack, or help to remove a condition, or bolster allied defenses, but we don't need to know exactly how he does any of those, because his tactical expertise must be fairly abstract to apply broadly enough.
Such things are the essence of the concept of the "leader" role that 4E systematized; and for that reason I think the Warlord class (perhaps by a different name?) should still be a class in 5E Next.
However, if that class is going to get a different name, what should the name be? Neither "Provoker" nor "Convoker" will work; "Cohort" simply means battle-comrade; "Proconsul" is a political/diplomatic position; "Veteran" needs to be available to all classes, and to unclassed NPCs; "Marshall" is a higher position, dealing more with strategy than with tactics; "Ensign" is naval and commissioned, not land-based; "Sparkplug" captures the spirit but refers to technology that didn't exist in medieval times; and "Coordinator" has too many syllables (5).
"Hotspur?" "Goader?" "Dean?" "Valiant?"
Better suggestions than those might help. . . .