Probably because there is no single definition.
I'll have a go at answering why it's important.
It's been shown that there is less social mobility at both ends of the scale.
That means that politicians, leading judges, CEOs of big businesses, the mega-wealthy and other powerful people tend to come from a limited pool. Not only do they control a disproportionate share of wealth, but they control everybody's lives. They are not necessarily more talented or able than other people. The Johnson family is a classic case of that phenomenon. Any society needs the most able to organise it and it doesn't have it, if some people have to fight to be given an equal chance.
Secondly, people at the bottom end find it extremely difficult to move away from the background into which they were born. They perceive the difficulty and give up, which becomes a self-fulfilling prophecy. Not only is their talent wasted, but they become society's "untouchables". They're in a minority and when the economy is under pressure, they are neglected. They don't have the resources to buy favours and their votes don't matter much. They become fodder for ridicule in the gutter press and are blamed for their own situation.
Such a situation is bad for society, apart from the ethics of abandoning people. Some of the people at the bottom end of the social pile are as intelligent as some at the top, but they're not given the same opportunities, hopes and aspirations.
I don't like Birbalsingh's analysis because, as ever, she tries to claim that others don't give those pupils opportunities, whereas she does. I heard her speak before she became famous and was a French teacher. That message came across then and she hasn't changed.