Same mAh, same volt - different current
I can see 5A, 10A, 20A or even more. Not getting what current matters here.

Because it matters? If you build e.g. a power tool (say, a power drill) that draws 15 A to make the motor powerful, what help would a 5A cell be?

I may sound rubbish, but trust me I have tried multiple articles but no exact scenario and answer.

Not rubbish, but you haven't understood that the current is a maximum rating.