I cannot reiterate enough that the owner’s manual needs to be read by everyone who owns and operates a car. There is more to vehicle ownership than putting gas in it and driving it. The owner’s manual will answer a lot of potential questions you could have, like this one, and inform you on how to maintain the vehicle, change a flat, check the oil, etc. I’m an ASE certified technician and I read the owner’s manual for every car I buy, and usually I learn something from it.
To answer your question, the blue coolant light is fairly common in VW, Audi, and some Toyota vehicles. It means the engine has not yet reached operating temperature and you need to drive the vehicle gently to prevent premature engine wear and damage. “Gently” means no full throttle acceleration, holeshots, or overly spirited driving. Once the light goes out, you can drive the car harder if you want without worrying about blowing up the engine in 15,000 miles. I do recommend against driving the car too hard, even after the blue light has gone out, if you want to keep it operable for any length of time without sinking a fortune into it.