Electrolytic capacitors are polarized. They work as capacitors when connected correctly, but present a short circuit (and can explode) when connected in reverse polarity. Therefore you can use eletrolytics only with DC, not with AC.
Now to this applicazion: to decouple the output of the driver to the speaker and let only AC pass, you use capacitors. And since the impedance of the speaker is very low, you need biiiiig (as in bigkim ) capacitance values. One cannot achieve the necessayr capacitaces with non-polarized capacitors (film, ceramic) - at least not with meanigful sizes and at meaningful cost. The trick is ti use electrolytics back-to-back as in this schematic. For each polarity only one capacitor is effective, the other one acts more or less like a short circuit. Since the capacitor with the correct polarity still blocks DC, no damage is done to the capacitors. See e.g. this discussion for more details.
One can also buy non-polarized electrolytic capacitors. These are internally built from 2 normal electrolytics back-to-back.