To avoid boring you with all the science, trainers like Nike Air's upset your foot's balance, positioning and control. This cushioned sole is soft and squidgy and generally has a high heel so the back of your foot is much higher than the front which isn't always the best position, yet there are times when this is useful but this is only accomplished through proper weightlifting shoes.
So the people in the know, what do they wear. Well 9 times out of 10 they will be wearing Converse all stars, probably the best, cheapest and long lasting training shoes available. However, you will also see them doing their big, heavy lifts like squats and deadlifts barefoot. This gets them close to the ground, especially with deadlifts so the bar has to travel that little bit less further.
The thing with Converse is that they are great for lifting conventional weights like your squats and deadlifts. But what happens when you want to do some Olympic lifting, Strongman work or conditioning work with the Prowler and various other sleds.
Well, they are pretty useless. You will have very little foot support, little grip and they are not a pure bare foot feel; which a lot of people argue is the best way to train. Which explains why people perform squats and deadlifts along with various other leg exercises barefoot.
For performing Olympic lifts, weightlifting shoes are the answer. They give you a high heel, are built very well so are sturdy and give you a solid planted feel which help you get that better form and push that little bit more weight. These types of shoes will help your performance and develop your muscles even better.

Do-Win 2010 weightlifting shoes

Adidas Power Perfect II
The only drawback with these shoes is that they are highly specific and only should be used on Olympic lifts and power lifts, and they are expensive. The Do-Win are the cheaper of the two and can be found for around £70, however the Adidas are £100. That's a lot of money for some training shoes that cannot be used for everything in the gym.
So what many people use, myself included, are bare foot designed shoes. These generally include Nike Free, Adidas Adipure and Vibram FiveFingers. I personally use the Vibram's and I think they are the best investment I have made in my training.

Nike Free

Adidas Adipure

Vibram FiveFingers
For me the Vibrams won the selection as the Adidas were not available in the UK and the Nike Free were reported to not be as stable.
The Vibrams have a rubber sole which grips on any surface, they are LIGHT, it feels like you have nothing on your feet, the strap systems helps lock them tight on your feet so your feet don't slide about in them.
I've noticed that the Vibrams have helped my training in nearly all areas. When lifting weights my feet are planted and grip well; and as they are bare foot your muscles, especially in your calves become more involved leading to better muscular development and performance. When doing strongman and conditioning work involving the prowler and speed sleds my feet grip so much better so I can run harder and push more weight on the sleds. Previously my feet would slip whenever I went really heavy and I could not push the weight, with these however I have zero issues. Also when doing Olympic lifts my feet are planted and grip the floor well.
The only area which I have found them to not great is running. I own the Sprint model (the one's in the picture) and they are extreme bare foot. Even though they are advertised for running, I would recommend going for a model with more support, maybe the KSO or Komodo Sport.
People don't like Vibrams because they look odd, they're expensive, some people even say they look queer. But at the end of the day it's about maximising your performance in the gym, and these do. These are the best shoes I have used in the gym and I doubt I will use anything else apart from other Vibram models. Training isn't about looking good or whatever else people think it's about; it is about PERFORMANCE, and the Vibrams have improved my performance, and I could pretty much guarantee they will increase your own too. Give them a try, you will not be disappointed.
Good Evening!