This can double the voltage swing at the speaker, compared to a speaker that is connected to ground. The ground-tied speaker can have a swing from zero to the amplifier's supply voltage. A BTL-driven speaker can see twice this swing because the amplifier can drive either the + terminal of the speaker or the — terminal, effectively doubling the voltage swing.
Since twice the voltage means four times the power, this is a major improvement, especially in applications where battery size dictates a lower supply voltage — e.g. automotive or handheld applications.