Earlier quoted context omitted.
It is a very, very British thing. A generation or two ago, almost everyone played it at school and it was Very Serious Business. I guess you needed something to occupy yourself before Pokemon Go was invented.
I have fond memories of playing conkers in primary school. Sometimes you got a rapped knuckle but children's sports is full of cuts and grazes, and it didn't hurt as much as slaps anyway. The main issue was that some kids would inevitably harden their conkers by putting them in the oven or lacquering them, and so on. But spotting that was part of the charm.
(When I was a kid, conkers were so prized we chucked sticks at them to try to get them to drop. So it was a bit of a shock to me when they started just being left where they fell. Kids today, off my lawn, uphill both ways, etc etc).