Hecarim is a Diver and squishy-deleting-esque style of fighter. Most of the big numbers you'll see from him come from his up-front burst with E -> Q (with bonus movespeed from Ghost/E before the E connects) while his W keeps him moderately health along with Courage of the Colossus. Trinity Force synergizes EXTREMELY well with him, hence why it's literally the first thing he will buy (even before completing his jungle item). He tends to go somewhat tanky after that (similar to how Darius will build a Black Cleaver and be done with his damage). While he does excel in extended trades in part due to his Q being on a very low cooldown after stacking it up, if he doesn't "scare" your team into retreating or do enough damage to be a threat he is mostly useless.
He is very binary in regards to what he wants to do, he will generally be looking to run straight into your squishiest member and attempting to chunk them for the largest amount of damage he can and force a winning situation. While someone like Jhin has very little to stop him from sitting on top of you spamming Q after his engage, their team is also down a member of the frontline while Hecarim goes in the back.
While ahead, Hecarim thrives on creating chaos quickly - being able to show up to a lane and run at them faster than they can retreat while simultaneously chunking them for a large amount. He HEAVILY relies on positioning mistakes and being able to knock the enemy squishy into his team (he doesn't run Flash, so his ultimate is the only realistic way to "break their ranks"). Anyone with a Taunt (Rammus, Shen, etc. provided they don't use it during his Ultimate as he is immune to CC effects during the charge) absolutely destroy him, as his E and consequently a large portion of his damage goes onto a poor choice of a target. Hecarim is a walking ball of stats, more or less.
When behind, Hecarim can't do much of anything well. He doesn't fulfill the role of a Diver then (unless you count suicide machine), and certainly lacks the stats to tank up a team for more than a brief moment. This is why he very "feast or famine" much like Olaf. He can't pull off a sick Lee Sin kick and single-handedly win the game for his team with a quick pick while behind, the enemy team can easily turn on him and melt him. He requires being ahead to survive early on to get the damage he needs to transition well. While he can, more or less, guarantee an early Flash by sprinting at someone with his Ghost/E combo, remember he is extremely mana-intensive. Without Blue Buff he will be OOM very quickly and he will probably have to back off after a single fight.
He has 357 Mana at level 3, while his basic E -> W -> Q (just one) costs him 142 mana (nearly 40% of his mana pool). This leaves him with just under 7 Q's left (not accounting for Mana Regen) that deal 50 (+60% BONUS AD - 15.3 bonus gives him a total of 9.18 extra damage for a total of 59.18) damage a pop before Armor reduction. While it looks insurmountable on paper dealing with that many Q's flying around, take a look at other champions for comparison. Ezreal's Q deals 35 (+110% TOTAL AD + 40% TOTAL AP) damage for 28 mana, while having 444 mana at level 3. If he E's away followed by W, he has 304 mana left, leaving him with nearly 11 Q's remaining that scale FAR better than Hecarim's abilities.
Hecarim is heavily balanced around being a mana-based Diver style champion with Trinity Force being his main life force. Try clearing on him without starting Blue Buff and watch how miserable of an experience it is - an OOM Hecarim deals nearly negative damage to jungle monsters and will be out of mana by the second camp.