What you want is called "skin". However, that's not something you just add on one day and go hiking for days. Keep in mind that our species evolved to get around by walking and running with our feet. Our feet have evolved to handle that. Unfortunately, habitually wearing shoes eliminates the stimuli that the feet need to produce the necessary thick skin in the right places.
The solution, if the desire is to be able to hike reasonable distances barefoot, is therefore to stop wearing shoes. Unfortunately, our feet can't respond to the new stimulus instantly. I like walking around barefoot, and do so whenever possible in the summer. I find it takes a month or so of significant regular walking over rough ground to build up the thick skin so that you don't care anymore. If you only do this occasionally, it will take longer, perhaps never even get to the full thick skin level.
So how do you get to the point where you can walk most anywhere barefoot comfortably without at some point pushing the limits of comfort? You don't. Your feet need the feedback that you consider uncomfortable to trigger them to build up the thick skin that makes it comfortable. Once you do though, you'll be surprised how much rough stuff you can walk over without giving it much thought. About the only thing I've never really gotten comfortable on is a bed of artifically crushed rock.
Once you regularly walk around outside barefoot, you'll probably be amazed at how much more you are aware of details in the ground. Different ground is at different temperatures, which makes sense but is generally not something you realize when wearing shoes. You also find that your toes start doing some useful things, not just stay lumped together with the rest of your foot inside a shoe. You will feel a lot more shure-footed too. I don't know how exactly to explain it, but you can feel that you will loose traction with bare feet before you actually do in a way that just doesn't match up to any sensation with wearing shoes. Shoes just suddenly slip. With bare feet, you can sense you are getting close before you slip.
I like walking around barefoot and make of point of doing so whenever the temperature allows it. Here in New England, that is roughly half the year. Unfortunately the feet loose the thick skin during the winter so you mostly have to start all over again every spring. I don't have a good answer for that.
I think it is unfortunate that our urbanized society usually looks down on walking around barefoot. This is to the point that many private establishments actually require you to wear shoes to enter them. Contrary to common belief, there is actually no law that says shoes are required in supermarkets. These are private property, so the owners have the right to set the rules, but it's wrong of them to claim state law makes them require shoes.
In the summer I keep a pair of sandals or "flip-flops" in the car so I can put them on when walking into a store I frequent. If I'm in a distant place where I'm not coming back any time soon, I sometimes have fun seeing what I can get away with. I get thrown out of the supermarket in Lincoln NH about once a year. It's interesting to note this has always been after I bought whatever I came in there for. Usually a manager comes over and tells me I need to wear shoes in the store as I'm paying in the checkout line or even after I've paid and am already walking out. I recognize they have the right to make the rules on their private property and I never resist when asked to leave, but that doesn't mean I can't have a little fun tweaking their nose every once in a while.