Most cyclists wear a base layer under their jersey. That's because the fabric of the best cycling base layers will be highly wicking, helping to transport sweat away from your body to the inner surface of your jersey, so that it can evaporate and help keep you drier.
The best cycling base layers come in different weights and it's a good idea to have a range that will work at different temperature ranges.
In summer, a short-sleeved or vest-style base layer helps keep you cool. A lightweight base layer may also add a little more sun protection, although if it's really hot many riders will dispense with theirs.
In cooler weather, a long-sleeved base layer can add more warmth, meaning that you don't need to add less-breathable outer layers over your jersey and will stay more comfortable. If you're building up moisture on the inside of your clothing, you can soon feel chilled and uncomfortable, and a base layer will help prevent this.