When you breathe out, you are expelling air from your lungs. This air contains a higher concentration of carbon dioxide than the air you inhaled, because your body produces carbon dioxide as a waste product of metabolism. When you blow this air into a balloon, you are transferring the carbon dioxide from your lungs into the balloon.
As a result, the air inside a balloon blown by mouth contains a higher concentration of carbon dioxide than the air outside the balloon. This can make the balloon feel slightly warm to the touch, because carbon dioxide is a greenhouse gas that traps heat.