Thresh is seen in many places- mid, top, support, carry- so it's odd to see him roaming around and farming the jungle. But why stick him in the jungle? There's a few simple reasons:

In sum:

The saves. The CC-Locking. Security. Not support/ADC/Mid/Top.

Ganks. Clears.

+The saves. A Thresh that keeps an eye on the map and his allies' health can save nearby allies from complete annihilation by a simple lantern toss. He can even swap places with them to secure a kill.

+The CC-locking. Thresh's kit is one of the most CC-heavy kits in the game. He can easily lock down enemy champions to keep them from doing anything while his team annihilates them. The Box is a massive slow that does a lot of damage, keeping everyone save Master Yi from maneuvering in fights.

+Security. Thresh can easily cause havoc in the baron or dragon pits, by jumping in with a powerful initiator ally( Wukong comes to mind), then throwing out The Box- he might even steal the monster with smite.

+Leaving other lanes open for champions who are better there.

Now, why would jungle Thresh be a liability?

-Ganks. His ganks, if you don't go hard and fast, are awful. He's the only character in the game who can be spotted when they walk into a wardless bush- the souls will start popping up in the lane, giving intelligent laners a chance to escape.

-Clears. The first clear is very dangerous for Thresh, and he's pretty easy to counterjungle if his lanes don't come to help him immediately. His clear times aren't too good until he gets to his Wriggles + Shiv combo.

For Jungle Thresh:
+Thresh can solo the blue buff, if he kites it properly. It takes a damn while, though.

+Don't Death Sentence to jump walls unless you're trying to escape! It's a waste of mana, and you'll run out of it if you do this with or without blue buff!

+Set up ganks ahead of time- otherwise, the souls will reveal your presence nearby. Gank hard and fast- you don't want to give the enemy a chance to escape.

+Few people expect you to follow their flash with your own- and then you use The Box. Flash-boxes can catch people by surprise, and can secure many kills your team would otherwise lose.

+Use The Box when running from fights or being chased through the jungle. It's like you literally put a wall in their path. It's less useful in lane, because they can walk around- but you're still forcing them to slow down.

+Keep an eye on your minimap for the enemy jungler- your counterganks are incredible.

+Ward. Ward your jungle, ward the enemy's jungle. Give their buffs to your laners, if they leave them undefended. Not only will this set the enemy jungler back, but your team will have four buffs.

+You can slip into the enemy's jungle unnoticed by flashing a wall and using Dark Passage to bring an ally over. Make sure it's not warded, first. Oracle's Elixir is good for this.

Against Jungle Thresh:

-Ward. Ward ward ward. You may think the souls keep you from having to ward. That's not true at all. You should ward when the enemy team has any members at all, because anyone can gank. Even Soraka.

-If you see souls in the lane, but don't see Thresh, get the hell out of dodge- you're about to be ganked.

-Start at his red. He has to start blue to first clear, so if you can secure his red, he loses a lot of XP and Gold, and he doesn't clear fast enough in the early game to steal yours easily.

-Don't get caught in The Box. There are three ways of doing this: play somebody with a way of moving through walls without breaking them( Talon, Katarina, Fizz, Kassadin), use Flash, or stand in the box and kill him if he's fighting you alone.

-Watch for the hooks. If you're paying attention and are moving at normal speed, you shouldn't get hit by Death Sentence.

-Don't flash until you know he doesn't have flash or The Box.

-Don't use mobility abilities when Thresh is visible and not casting Death Sentence, Flay, or The Box.

On either side, it's better to start Blue- you need the mana for the first clear. Get a smiteless leash, then clear Wolves and Wraiths- level 3 will help if the enemy came to counterjungle. If you're certain there's nobody coming to steal your buff, take red, and look for a gank. If there isn't one, keep farming and watch for an opportunity to use Dark Passage or Death Sentence.

Ganking can be difficult for Thresh when he doesn't have his mobility boots. It's generally best to initiate with Death Sentence, and maybe a Dark Passage to get your laner up to the enemy. If you have it, use The Box, then Flay- you might cause them to miss their flash if you use this combo in this order.

On any lane, you can also have your allies bait their opponents into your combo.