The key features of minimalist or "barefoot" shoes are:
- They are zero-drop (meaning the soles are flat, so there is no drop from heel to toe and no arch support)
- They have a wider toe box (this means your toes can flare out in the shoe, and sometimes this makes them look a bit like clown shoes)
- The soles are generally a lot thinner and much more pliable than those of typical shoes, and as such they don't provide quite as much protection (the point of that is that you can still feel the ground beneath your feet and maintain a lot of intricate mobility)
For example, the thicker heels you see on most boots and shoes today mostly originated in the US from cowboy boots, which of course were designed for horseback riding, not walking or running. A lot of people thought the design looked cool (and probably liked the idea of seeming a bit taller), and the rest is history.
Sadly, these modern shoes mess up our foot development considerably. They smash the toes together, which are supposed to flare out and help a lot with balance. The thick clunky soles make it impossible to get any detailed sensory feedback from the ground, so all those nerve endings in the foot go to waste and you clumsily stomp around, putting excessive strain on your joints from the force and increasing the likelihood of rolling your ankle from a misstep. Related to this is that they cause a lot of people to land on their heels while running, which is very bad for reasons that are easier to show with a picture (see below). They also prevent our feet from developing the toughened (not necessarily callused) soles they are supposed to have, which, believe it or not, actually do provide some significant protection against thorns and little sharp rocks. All arch support does is encourage flat-feet by giving the foot muscles no reason to maintain that arch on their own.
Overall, in these harmful shoes your feet become weak and ever more dependent on them, and you can probably see how all this would in turn be a factor in other issues like posture and back and neck pain. Your whole foundation is thrown off, so the whole stack of bones and connective tissue has to compensate for this imbalance with a lot of tightness where it shouldn't be. It's a bad situation that almost all of us are in without even realizing it.
But the good news is that it is reversible to a significant extent, though the transition could be difficult depending on how bad it is. It's certainly not easy to undo decades of improper treatment of the feet, and it's important to say that because someone could take these difficulties to mean that the problem is the new shoes and not the old ones. For those who have children or who will have children, please do your research and get your children wearing proper footwear so they don't ever have to deal with this problem.
Improper running caused by thick-soled shoes (harmful to joints and wastes energy) vs proper running (which is generally instinctive when totally barefoot as heel striking barefoot usually hurts); notice how the angle of the shin to the ground in the first one sends the force of the strike backwards horizontally into the knee and hip which harms the joints and slows the runner down; contrast that with how the runner with proper technique on the right is falling slightly forward when landing, thus utilizing gravity to keep forward momentum and save energy
If you want to learn more this is a pretty solid presentation: