Trebuchets are similar to Catapults in that they possess similar attributes, however Trebuchets are far more advanced than Catapults. They can hurl rocks much further than Catapults and are also much more accurate.
However, once setup, Trebuchets cannot be repositioned on the battlefield- your only option would be to disband them and to recruit new ones from your Siege Camp. Three Engineers are used to man the Trebuchet instead of just two used on a Catapult.
Trebuchets can also be setup behind defensive structures and you can fire them from there as well. You will however need to pay slightly more attention just to ensure that you do not hit any ranged units within any nearby walls or towers. If a Dairy Farm is placed in your Castle, you will also be able to hurl dead cows over the walls of enemy castles in order to spread disease. Changes will sometimes take a few minutes to filter through, so this will not be an "instant" availability.
Trebuchets can destroy buildings (both Stone and Wooden), walls, towers, gatehouses and other parts of enemy castles, as well as potentially any enemy units that are targeted. Trebuchets can also outrange tower mangonels and and tower-mounted ballistae due to the distance the Trebuchet can hurl rocks or cows. Note that when diseased cows are thrown over the walls, it can create piles of gong. These will obviously affect the peasantry of the enemy castle but have little to no effect on the military units defending it.
Trebuchets are by no means as accurate as catapults, but you can still hit a wide variety of targets with them, and it is a lot easier and safer to take down walls, towers or other fortifications without being attacked yourself, particularly if you keep ranged units near your Trebuchets. It also has a slow rate of attacking, often making sieges long and brutal. Note that the Trebuchet can also be taken out by other longer-ranged missiles such as Fire Ballistae or even an enemy Trebuchet.
You can recruit Trebuchets from the rank of Duke. You will need 200 gold as well as 3 peasants from the campfire before you can recruit a Trebuchet. You will also need to place an Engineer's Guild before you can recruit any Trebuchets from your Siege Camp.
Tip: An excellent tactic when using Trebuchets is to create Siege Camps at several locations around an enemy estate, for example different directions you can arrive from. Recruit several Trebuchets from each one, and then let them all decimate the castle of an emeny from where the Siege Camps are located. All you will need to do is make sure the Trebuchets are adaquately protected against ranged missile fire. You will likely find that you can reach most if not all of the estate through all your Trebuchets.