Versatility

Thresh can quickly and easily change his role mid-game with no complications. If someone falls behind, especially the ADC, Thresh can pick up some major slack for him/her.

Support

Thresh can support early game support late game with no problem. Building cool-downs, auras, and mana keeps Thresh's abilities able to suppress enemy carries, save teammates, and secure kills late game as effective as early game.

Tank

Thresh can throw himself onto the enemy team and use his ultimate to initiate VERY well, especially if he is tanky. Tanking as Thresh is very effective because of his fear factor. Thresh's CC is very potent, causing the enemy team to focus you. In doing this, your team can successfully focus key champions on the other team and win the team fight.

Damage

When your ADC falls behind, its easy to pick up damage. Flay with then become your main source of damage with the passive heaving out massive pokes and the general damage it does. The aggressive abilities that Thresh has in his kit allows for general damage output and the ability to pick up some of the ADC's slack.

Pros

Great Kill Secures
Good Saving Potential
Great Harassment
Great CC

Cons

Long Cool-downs
Difficult Laning against people with high poke potential (Cait, Sivir, Ez)