A lot of things, of course, but two really BIG things:
1.) Attitudes towards Sex. Neil Simon’s Come Blow Your Horn has a scene where the female lead, in order to call the male lead’s bluff, offers to walk right into his bedroom and have premarital sex. Everyone acts as if this would be an unthinkable thing, to be avoided at all costs for the sake of mores and society and decorum, and acts to prevent it. Just a few years later that scene could not have happened. Today, I don’t think kids would even understand it.
People talked about it, before, of course. Playboy became a big seller by presenting the lifestyle of unfettered and carefree young folks, engaging in pleasurable sex whenever they wished to, but when Playboy started publishing 50 years ago, it was a pipe dream for most people. Premarital sex and cohabitation were done on the sly, not openly. Times has changed.
2.) Computing power. When I was a kid our family got invited to a company presentation where they gave away, as souvenirs, little pieces of magnetic tape from the computers. A computer was a huge, bulky, unwieldy, expensive thing. Hand Calculators became available when I was in high school, but the glitziest thing an affordable one could do was square roots. I stuck with my slide rule, which was cheaper and faster (An HP-35, which could do trig and log functions, cost $395). I continued to use my slide rule for my first two years of college, until the HP-25 came out for $195. A friend built his own computer, with a hard drive scavenged from a mainframe – it was as big as a refrigerator. I programmed on mainframes until my senior year, punching instructions and data on punch cards. Programs and subroutines filled entire drawers. God forbid you should drop your pile of cards and get them out of order.
I still read in reprinted science fiction stories about rocket guidance using cams (!!!) (See Heinlein’s Rocket Ship Galileo or George Smith’s Venus Equilateral, both still in print in the 1960s and 1970s). If there’s one thing the old SF authors failed to predict properly, despite the ubiquity of robots, it was the pervasive and powerful influence of computers. (Although, surprisingly, quite a few effectively predicted the Internet.)
Today, of course, the small size and huge capabilities of computers are evident. They have transformed several fields, and I think that people even today would be hard pressed to do some of the things that were done until the 1960s totally without the aid of computers. Navigation, guidance, optics calculations, artillery ranging, iterative calculations, making change, keeping accounts, banking, library systems, cataloguing, inventory. Imagine doing this nowadays without computers. Damned near impossible.