Jarvan is a champion that has gone through many nurfs. He used to be a god in the jungle and in lane. This is not the case anymore yet he is still very viable.

Jarvans job as a jungler is to gank the lanes heavily and be a sacrifical lamb mid game. You buff your team with flag and initiate fights. Then 9 times out of 10 you die.

Going to steal a stonewall008 video again. Much respect because his videos are great for introducing champions to people.
http://www.youtube.com/watch?v=eOdL4mLcUqs&feature=player_embedded

This is a replay of jungle jarvan in High level play. CLG vs TSM
http://clgaming.net/replay/2451/

I use standard armor pen for a jungler which is keeping around 12 armor pen. This is due to the fact that most of the creeps in the jungle have sub 12 armor. I use flat AD for quints and mix some flat ad reds in as well due to Jarvan's nice AD scaling on his ult and q.

Yellows are optional you can either use armor or dodge yellows, this is all preference.

I use magic resist per level blues for late game tanking.

I use 1/13/16 for masteries. The reduced minion damage in the defense tree is important if you are going to start regrowth pendant. The rest of the masteries aside from increased one xp is optional.

Jarvan used to be able to jungle quickly with just gp5. Now though I feel you have to get a madred after your philo stone.

I start regrowth pendant and 1 health potion. You must get a very strong pull on blue if you are going to do this build so keep that in mind.

After I do my clear on jungle I pick up philo then go back to jungling/ganking. Pick up boots and madreds then heart of gold if it is sub 11 minutes. If it is not sub 11 minutes then grab your phage and a banshees. Finish trinity and then go for atmas after that. It is very unlikely you will finish the build and the tanking items are all dependent on how fast you are farming and the types of damage the enemy team has. If you are farming very poorly build tank over finishing trinity.

A perfect end game build though would be Wriggles>mercs>Trinity>Warmogs>atmas>FoN like I said though you most likely never get this though.

I grab e first due to the increased armor and attack speed plus aoe damage it gives for jungling. I grab 1 point in q as well as w after that.

I will max E first then Q then W. Your bread and butter damage combo is your flag toss plus javelin so practice being able to hit this 100 percent as well as leading targets with them.

Throw your e slightly ahead of where a person is running then Q to it to hit. If you don't your flag will usually hit behind them and you will miss your knock up.

I use flash smite for catching people. You can even use exaust or ignite because Jarvan has a built in blink.

You have two options with jungling Jarvan. You can go cloth armor 5 pot and run this exact route with a strong pull on blue.

http://www.youtube.com/watch?v=Tz21FXGmxsc

Or you can run regrowth pendant plus plus health pot and have an extremely strong pull on blue then take wolves. After this you can clear wraiths+double golems OR you can go and gank mid or top lane.

To gank mid make sure you let mid know you are ganking. Have your mid open with any cc they have then flag toss slightly in front of the enemy champion and q to it. Auto attack them twice and most likely they will flash after this. BE READY TO FLASH WITH THEM and finish them off if they are low enough to die in 1-2 auto attacks.

For top gank if you are blue side you will walk through the top triangle brush and gank the person from behind with flag toss q combo.

Usually these ganks wont kill this early unless the person is dumb but it will blow summoners meaning if you gank that lane again within the next 2-3 minutes that person is a guaranteed. kill.

Once you have enough gold for your philo stone from jungling go back and buy that then continue clearing small camps and constantly ganking lanes in between. Jarvans strength as a jungler is it costs him very little to gank and he can do it over and over.

Basically jarvan is a throw away initiate. You jump on their carry and start fights if they are out of position. Usuaully you will die if you dont flash out fast enough or are not farmed enough. This will start a fight and usually kill the enemy carry if your team follows up.

Jarvans role all depends on how well you farm early.