A horde is a large group of zombies. In the game, hordes can be spawned as well as players grouping them together.
Player-Made hordes, otherwise known as trains, are groups of or individual players- experienced or not- that form a train to circle groups of zombies to secure kills for cash. It is a crude but effective method to obtain cash. (NOTE: Try not to be rude to others outside of the train. It doesn't matter if they're trying to get kills, you don't own the kills.)
You are advised to not walk the opposite way as the train, it will either cause you to suicide and/or cause any zombies straying behind you to assassinate the player leading the train.
The player who made the train may or may not want you to 'steal' kills by simply shooting into these trains. Please note that kill stealing is only valid if you kill someone's target as they are shooting it. If they haven't fired and hit the zombie yet, it's anyone's kill. Nobody is entitled to a kill that they haven't even attacked.
The most common sign of an incoming zombie horde is accompanied by a loud siren and zombie growls. They will most likely spawn in the bridge. Typically, these hordes are in close proximity in groups of over 10, so caution is advised when approaching.