ST Analog Switch Booster
The manual only says that the booster must be enabled for ADC operation below VDD of 2.4 V, and disabled for VDD above that.

I'd hazard a guess that it's a charge pump used to generate a higher voltage for the analog switches used in the ADC. Generally these switches have a lower on resistance when driven from a higher voltage. 

I can imagine the conversation amongst the designers. The entire circuit works over the range 1.7 V to 3.6 V except the ADC, which only works above 2.4 V. Do we ditch the ADC, or ditch the lower half of the operating voltage range? Wait, I've got an idea!