What is cooperative gameplay?
Co-operative (or co-op) gameplay is when two or more people run a company using the multiplayer system, working together to achieve the same goals. This style of gameplay requires great skills, as you have to know what other people are doing all the time, and make sure you don't use up too many funds.
A good example of teamwork in action would be one person placing the rails for a dual-rail route, and the other player adding signals as they go along. Co-operative games can lead to fast development of the company and the routes. Two pairs of eyes are always better than one.
Who plays it?
Anyone who wants to. However, a group of players at openttdcoop are best known. For more information visit their blog , wiki  or have a chat on IRC OpenTTDCoop OFTC IRC Web Chat.
The team came up with a new proposal of a "cooperative but competitive" gameplay in mid 2006. A lot of ideas around this concept are written down here.