Some people choose to cycle in comfortable cotton clothes. There’s nothing wrong with this, and if you are a casual cyclist then you’re unlikely to have any problems; however, cycle jerseys etc exist for a reason, and that is because they are optimised for the whole business of cycling.
When riding over long distances or in the hot weather sweat can become a problem. Jerseys address this problem, and are constructed so as to alleviate sweating.
Technical fabrics draw sweat away from your skin, where it evaporates in the open air. By contrast, a cotton t shirt may become heavy with sweat over time.
Professional cyclists have to take various bits of kit with them when they cycle. For instance, hydration packs are taken along, for obvious reasons. All this stuff needs to be stored, and so many modern jerseys have several pockets which are used for carrying gear.
When you cycle, you may encounter a range of temperatures or environmental conditions. With this in mind, modern jerseys allow you to adjust the ventilation of jackets, by allowing riders to open or close zips. When riding over large distances this can really make a difference to comfort and performance.