Extremely generally speaking, I think women tend to be more “people people” and men more “things people”. Women listen in a convo to get how the other person is feeling and how they view things, so they can relate and say comparable things and there can be a meeting of the minds. Men listen to analyze what’s being said, to get the concept that’s coming out of the person’s mouth without so much regard about the person’s psychological status.
A woman's more likely to say "I understand! I know just where you're coming from!" where a man maybe more likely to say "Well, here's my advice on what I'd do about that".
I figured while in my first anthropology classes, before I was aware of evolutionary psychology (there were no classes in it at the time), that if you know how people would have to be to survive as hunter-gatherers then you know how people basically still are now. Women don’t roam the savanna stalking a prey, they stay in a group and need to be in constant verbal contact with one another, and feel how the others feel in order to keep things cordial. You see it today in a group of 3 or 4 woman carrying on two conversations between each other at the exact same time, any one of them able to switch instantly from the one convo into the other one and then back. (Among the most mind-blowing things I’ve ever seen!)
Guys might go hours without talking, and they probably have a less strong impulse to be texting with friends while alone (like, for example, while driving a car). Their convos may be a bit less spontaneous and less nuanced to account for feelings (I've always admired how diplomatically women speak without it seeming 'studied' at all), and nonverbal cues work when words seem needless and they tend to plan in advance what they’re going to say and what direction they think things should go. There’s often an aim beyond just a “meeting of the minds”.