Have you were won a battle in which only 5-10 men are left in each of your companies (not counting the ones that were destroyed or retreated)? Ever dig into a battlefield's small decoration village to funnel the enemies men into a choke point to wait for your reinforcements to arrive? Ever used flanking maneuvers to position you cavalry on both sides of the enemy's regiment and used a pincher maneuver? Have you ever won a battle while being outnumbered or ambushed by using split second retreats, charges, and effective terrain exploitation? Did you ever win the historical battles? Have you ever been forced to control a small main force and wait for the larger supporting force to reinforce you? Have you ever tried sallying forth? Have you ever had to control your main force as well as 3+ reinforcing regiments that couldn't quite join you in time? Have you killed a traitorous general using his own ex-partner general that you always brought with him? If you have done any of these and won, you have achieved this. It is so satisfying to see that "famous historical battle" icon on the map that stays there for the rest of the campaign.
It's awesome playing with a mere captain and doing so well, that he is offered a promotion to full family membership.
Put together an army of a few stacks of infantry, and a whole load of catapults and trebuchets, and then attack or defend against a superior force on a bridge. Set your catapults to use flaming missiles and let the enemy repeatedly charge shoulder-to-shoulder down the narrow bridge. Watch as the enemy burns to death by the hundreds and your siege unit experience levels max out from zero in a single battle. It is absolutely possible (and extremely entertaining) to defeat two thousand men using less than five hundred in this way with no losses.
It is possible to have a peasants with nine experience and upgraded weapons (that's the max they can get). Do this in custom battle and pit them against three enemy units of inexperienced peasants with no upgrades. Spread your peasants thin to get a surround, bunch them up to form a tight circle, put them in trees, on a mountain, and/or in a choke point. Using the right strategies, you can win the battle with three to one odds.
Killing the King of an enemy faction in battle, especially with low-tier units. It's especially gratifying when you see the demoralized knights and archers fleeing from the badass army of town militia who just defeated their lord.
While it might be annoying in the short-run, staying in the Pope's good graces, by scrupulously avoiding unprovoked war with Christian factions, can reap huge benefits for your faction. Get yourself a couple full-stack armies and wait for a neighboring faction to be excommunicated. Then, convince the Pope to declare a crusade against that neighboring faction. Watch as they are caught completely off-guard as six different countries declare war against them, throwing their own campaigns into disarray and irrevocably shaking up the balance of alliances. Once the dust has settled, you could end up with impressive territorial gains, a huge financial boon due to both papal favors and reduced upkeep of crusading armies, and an increase in the Pope's opinion towards you. That would lead to more cardinals of your faction, meaning more Popes of your faction, and more crusades against your enemies. You will end up feeling like a Magnificent Bastard who can sway the course of European politics. Your generals will become paragons of chivalry, your economy will grow, and you will effectively rope the Church into bankrolling your expansionism.
You'd think Scotland, a faction with excellent infantry but relatively weak cavalry and archers, would fare horribly against the Mongols and their armies of horsemen, right? Yes... but only in an open field. Take a few fully upgraded Noble Pikemen, Noble Swordsmen and/or Highland Nobles in a castle defence against a huge Mongol army, place them in position at the gate, and then simply sit back and watch as the most feared and effective military force since the Roman legions throw themselves at your armoured bulwark and fall in droves.