The root of the word modern seems to mean "of the present time," so in that sense both the hipster living in a NYC condo and the hunter gatherer in the Amazon rain forest today are equally "modern." Like nearly all words, though, the word has many meanings, some of which are intended to praise new or approved changes in society.
I will use it in just that sense.
To me, one of the dominant social changes of the past couple of hundred years has been the emergence of rights for marginalized social groups and especially for women. It's easy to forget that less than 100 years ago, women could not vote in most of the US, couldn't vote even a few decades ago in even such a modern state as Switzerland. Of course women remain severely restricted and oppressed in much of the world even today.
The change has been traumatic for many traditionally male dominated societies. The Ayatollah Khomeini apparently became exercised enough to enter politics because women were going to be allowed to vote in the Iranian parliament.
Many other disadvantaged groups have matched or followed the tactics and successes of the Women Liberators: Blacks, other persecuted races, homosexuals, minority religions, and even sex workers.
For me, those developments are the essence of the "modern" transformation of society. Educating women is a crucial component that is still transforming the world.