Archers are the standard missile troops in Stronghold 2. They are a much less powerful version of Crossbowmen, and do not wear Leather Armour of any kind to protect them from arrows. Due to this fact, they are a fast and mobile troop, and can easily run around the map at speed. However, they do have a much longer range than Crossbowmen.
You can recruit Archers from the rank of Knight, and you will also need a Bow to recruit Archers. These are produced through the Fletcher's Workshop, which also becomes available at the rank of Knight. Due to the lack of protection by Leather Armour, Archers can be killed by Crossbowmen in a single shot, and an encounter with Horse Archers can be catastrophic if not handled with extreme care- especially considering Archers must be stationary to fire.
You will also need a single recruit from the campfire before you can recruit an Archer, as well as Honour. Honour can be produced by the means shown in this article. Archers are good units for your walls to protect your walls against invaders, and are also good units to help protect your neutral estates against attack as well.
Tip: Archers can be incredibly effective in dealing with Armoured units, such as Knights- but only when in numbers. If you're caught out in a situation where you may need to face hand-to-hand combat, keep withdrawing a section of your Archers that is closest to the immediate enemy far enough that they won't be attacked, but not too far so that they can no longer fire. Periodically pulling back your troops in this fashion can greatly help in defeating armoured units.