The green lights are a countdown to the next service. The yellow indicates that the service is due now. The red indicates that the service is overdue. The on-board computer works out the service intervals by taking into account several variables such as the current mileage but also, and more importantly, the way in which the car is driven. If you drive it with your foot to the floor all the time, the service intervals will become a lot shorter.
BMWs have three main types of servicing: Oil, Inspection I and Inspection II. The cheapest being Oil, and the most expensive being Insp II. The servicing sequence goes: Oil, Insp I, Oil, Insp II.
After about 60,000 miles it becomes less and less practical to take it to a BMW dealer for the servicing, unless you can afford it. Taking it to a BMW specialist is a very good idea as they will carry out the servicing to the BMW Schedule thus ensuring a proper service and at a reduced cost. But, due to the nature of BMWs its not a good idea to take it to a place that's not a BMW specialist.
Newer BMWs give a service countdown in actual mileage rather than coloured lights.