What does $200\%$ faster mean? (How can something be more than $100\%$ faster?)

"Faster" refers to speed (units of something per unit of time) or velocity (units of something per unit of time, with a directional component).

In this case you are talking about charging a battery in $5$ minutes. The speed of that operation is $(1.0\,\text{battery})/(5.0\,\text{minutes})$, or $0.2$ batteries per minute.

$100\%$ faster than $0.2$ batteries per minute would be $0.4$ batteries per minute, or charging a single battery in $2.5$ minutes.

$200\%$ faster than $0.2$ batteries per minute would be $0.6$ batteries per minute, or charging a single battery in $1\frac{2}{3}$ minutes, or $1$ minute and $40$ seconds.