PWM is Pulse Width Modulated. The charger takes the incoming AC, and rectifies it into a DC bus. It then switches the dc connected to the battery on and off really fast. Really fast meaning anything between 1KHz and 100KHz. The amount of ON time vs OFF time causes an average voltage to appear, and the charger controls that voltage based on how much charge the battery has. The end result is that the charger varies the average dc voltage to the battery, so that it charges properly.
The battery is really good at absorbing low frequency signals. The switching transients, which happens when the dc changes from ON to OFF to ON, create very high frequency signals. These signals can couple to other wires in the area, which can cause problems with sensitive equipment in the area.
Most of the time this isn't an issue. But it can be. A battery charger can cause the same kinds of problems that a Variable Frequency Drive (VFD) can cause. The larger the current, the larger the potential noise problem.
It's cost effective, it's very popular, and it drives us amateur radio enthusiasts nuts.