Skill at a widely popular game, hobby, or sport, deemed necessary for social interaction.
Time was, most leisure time activities (for the middle and upper classes) could be summed up in a short list: playing piano or singing, gardening, collecting (art or antiques), fishing, cards, billiards, dancing, golf, and tennis, with, perhaps sailing, shooting and rowing for the more ambitious. Everyone had been exposed to at least a few of them, in one way or another, and so one could expect to be able, given a random dinner companion, to be able to discuss, for instance, the third hole at St. Andrews with some confidence, or to plan activities for a party beyond standing, talking, and drinking: given a piano, or a folding table and some cards, a good number of guests would know what to do with them. To which end, most parents would teach or get their kids to lessons on these subjects, not to make them dancers, pro golfers, or bridge champs, but because they'd find life more interesting if they could share in these activities (whether they were passionate about them or not.)
Nowadays, it's not quite that simple. For one thing, there are a lot more hobbies out there (each with its own jargon, celebrities, etc.), and people aren't as conformist as they used to be: whether you're a skater or a biker isn't because you or your family come from a skater or biker set, but because you like them. Also, since about the 1980's a certain spirit of professionalism has invaded our leisure hours: it's not enough to casually put on one's comfy shoes and go for a stroll in the park, you're either running/jogging/speedwalking (with appropriate footwear) or hiking, meaning that you intend to stay awhile, striking out where the hand of man has ne'er set foot. Just dicking around outdoors, looking at the ducks in the pond and watching the seasons change isn't going to impress people, while a highly technical account of your ascent of Worthless Boulder is going to bore the piss out of them.
And one wonders why no one can talk to anyone nowadays....