The bourbon can be distilled up to max 160 proof. Then diluted with water down to 125 proof to enter the barrel. Water molecules are smaller than alcohol molecules. Therefore, they escape the barrel much easier when it’s hot, especially at the top of the rickhouse, hence concentrating the alcohol and driving the proof up. The longer the aging, the higher it can drive up the proof. From 125 up to 150. In contrast, barrels at bottom of rickhouse are cooler and moisture will enter the barrel and proof down the barrel.
Note, it doesn’t have to enter the barrel at 125 proof. That’s just the max. Many quality bourbons enter at less, Pappy at 115 for example