What is a heart murmuring, and is it a condition which is serious?

It depends. A heart murmur is an extra sound that is not normally heard when listening to the heart. There are many situations where the murmur is normal and it is referred to as an "innocent" murmur. Alternatively, the murmur may be due to abnormal valve function, an abnormal blood vessel or a hole in the heart. It is important to have an evaluation to know for sure.
Leaky valve. A heart murmur is a leaky heart valve. It can be functional, meaning it has no effect on your activities or it can be serious, perhaps needing surgery. It is best evaluated with an echocardiogram or ultrasound of your heart. I have had a functional murmur since i was a teenager and have no problems. My mother needed an aortic valve replacement. So there are many different murmurs.