If you started out running in the same clothes you'd wear to redecorate your house, you will have quickly realised what clothing manufacturers have known for years: when it comes to running, cotton won't cut it. Or rather, it will - your skin will be rubbed raw from the damp, heavy T-shirt clinging to your body. You might also find that you overheat - or freeze when you stop and the T-shirt won't dry out - and the flapping fabric is about as aerodynamic as a bouncy castle.
T-shirts made from technical, man-made fabrics are designed to avoid all of these problems. Even a basic running tee will be made from light wicking material (to draw moisture from your skin and dry quickly) and have flat-locked seams to prevent chafing, with a generous cut around rubbing hotspots like the armholes and neck. As with any kit, the more you pay, the more technical features you get: top-end tees are often seamless (welded rather than sewn), treated with anti-odour chemicals, and cut for a 3-D shape so they're easier to run in.
While the raw materials of most T-shirts are similar, manufacturers have developed different weaves to react to temperature changes, changing the airflow around your body to keep you comfortable.