Let's take a loot at Malphite's passive and abilities.
Passive: Granite Shield
I don't believe that too many people recognize just how ridiculously good this passive is for Malphite as a jungler. Malphite's base health, with masteries included, is around 550 at level 1. Pretty solid for a jungler. WIth his passive though, Malphite has a continually refreshing extra 10% health. So, at level 1, the most difficult level of jungling, Malphite has an extra 55 health, bringing him up to ~600 health. This is beautiful in terms of trying to clear camps because of the extra tankiness. This passive is also ridiculous in the late game because you'll end up with around 3000-3500 health when decently itemized, meaning a passive shield of 300-350 extra health. That's 3300-3850 health. Nothing to mess with.
Q: Seismic Shard
This is your pre-6 ganking ability, as well as your chasing ability. Malphite takes the movement speed of an enemy unit, reduces it for 4 seconds, and adds that reduction to his movement speed for the same amount of time. This basically allows Malphite to catch whatever unit he's chasing. Also, Shard allows Malphite to harrass in teamfight dances and under tower. Typically, you want to max Seismic Shard second. This gives you the ability to chase down enemy champions solidly until your level 3 scaling of your ult (maxing the cooldown on it). Take your first point in Seismic Shard at level 3.
W: Brutal Strikes
This is your starter ability when jungling. Passive splash damage is extremely useful in clearing out wolves or wraiths before hitting your buff, and actively, Malphite also gains increased armor and damage for 6 seconds. Perfect for clearing early camps. This ability, though, doesn't have much more effect until late game. You're going to be building armor naturally on Malphite, and his attack damage isn't exactly why you picked Malphite to jungle with. Nevertheless, make sure to activate this ability when ganking to buff yourself up a bit against damage, and to put down some damage of your own. Take your first point in Brutal Strikes at level 1, but max it last out of your abilities.
E: Ground Slam
This is your camp-clearing ability, and it also spells death to champions who rely on attack speed to do damage. Ground Slam deals AOE damage to every unit within 400 of himself, and reduces their attack speed by 30%-50%. This ability scales on both armor and ability power, two things you'll see prevalence of in the build. In terms of jungling, Ground Slam allows you to punch through camps while taking a lessened amount of damage by reducing the attack speed of camp monsters. In teamfighting, keep activating this right next to the opponent's AD Carry to shut them out of their own damage. And you're Malphite, so you can survive sitting right next to the ADC. The longer the game goes, the more devastating it is for the opponent's ADC to take a 50% attack speed reduction. As the game goes on, Ground Slam becomes less about damage and more about attack speed debuffing, but that's not to say that you can't chunk enemy health bars with this ability. Take your first point in Ground Slam at level 2, and max it first.
R: Unstoppable Force
The name speaks for itself. Unstoppable Force turns Malphite into a bullet train of raging rock-hard AOE knockup and damage. The utility of this ability, though, is what makes Malphite's ultimate so hard to deal with.
1) Initiation --- Unstoppable Force is a terrifying way to start a teamfight. In knocking the enemy team up, you have essentially held them down for 1.5 seconds for your team to absolutely go nuts on. If you and your team are doing it right, the enemy team's carries should die within 2-3 seconds of activating the ult. Also, because you're Malphite, if your lane is set up correctly for it, use unstoppable force to kill enemies under their own tower. Towers don't hurt Malphite, they just tickle him. Let your carries go crazy on enemy champions while you eat the turret aggro.
2) Counterinitiation --- Unstoppable Force also can really punish an enemy team for engaging. Waiting for the perfect moment when the enemy champions are close enough together, then ulting right into the middle of them, can turn a teamfight completely around in an instant. Punish them for trying to dive onto your carries.
3) Chases --- This one you're probably lost on, so let me explain, but before I do, let me say that if you're not good at predicting the directionality of enemy escape moves, don't try to pull this aspect off until you're better at it. That said, Malphite's ultimate is incredibly good for securing the kill on low enemy champions who have flashed/blinked/jumped/dashed through walls to try to get away. If you know the direction they went in, use Unstoppable Force to go after them, then combo off the Q/E/W to make sure they don't get away. Again, if you don't feel confident with your ability to predict directionality of those escapes, save the ult. Unstoppable Force has a sizable cooldown unless you build decent cooldown reduction.