Most cars have a light on the instrument cluster called the check engine light. The light comes on at different times when triggered by the vehicle's computer to indicate your car needs to go in for service. A BMW check engine light works the same way, and while it does not mean a breakdown is imminent, it is important to have the car serviced.
Cars still under warranty often need regular service to ensure the warranty stays in force, and a BMW check engine light activation stays in the car's computer until the tech resets it. If the car has a failure related to the code that activated the CEL (check engine light), and you continue to drive it without service, it could affect the warranty coverage. You could end up paying for the repair out of pocket simply because you didn't take the car in and have the tech check it.
More often than not, the CEL does not indicate a catastrophic failure, but you could have drivability issues or a poor running engine related to whatever activated the light. In many cases, a bad sensor will cause the light to come on, and there may not be any real issue with the engine, but the sensor sending false information to the computer could affect how the vehicle runs and drives.
One sensor issue that causes a check engine light activation in many cars is a faulty O2 or oxygen sensor in the exhaust system. The O2 sensor reports the makeup of gases in the exhaust as it leaves the engine, allowing the computer to alter things like the fuel/air mix or the engine timing to improve fuel economy and performance.
A BMW check engine light activation does not require you to go to a BMW dealer for service, but the BMW dealer can pull more information out of the computer to determine where the issue is in the car. Most repair shops have computers to read the codes, but sometimes they can be challenging to decipher if you do not work on these cars daily.
If the repair shop you use specializes in imports and European cars, they will often have the tools and knowledge to find the faulty sensor and fix it. However, this is not a repair for an oil change or quick lube shop. Look for a shop with certified techs with experience in BMW vehicles, or take the car to the dealer so you are sure the work is done correctly and high-quality replacement parts are used in your vehicle.