Power
Rated power of the subwoofer. Technically, this is the highest average (rms) sound power at which the device can work normally (without sound distortion and damage to components) for an unlimited time. Simply put, the more powerful the subwoofer, the louder it is. The choice for this parameter depends primarily on the size of the space / room that is planned to be covered; detailed recommendations for different situations can be found in special sources.
Also, the power is directly related to the characteristics of the amplifier used with the subwoofer. For active subwoofers (see "Type"), this item actually indicates the nominal power of the built-in amplifier; the speaker itself can be more powerful, but it doesn't matter anymore. For passive models, the power rating corresponds to the highest amplifier power that can be connected to the speaker without the risk of damaging it at high volume.
Frequency range
The range of audio frequencies reproduced by the subwoofer. As a general rule, the wider the frequency range, the richer the sound and the more detail the speaker can convey. However, it is worth remembering that subwoofers as a class are designed for low and ultra-low frequencies in the range from 20 to 150 (sometimes 200) Hz. Therefore, in fact, a significant difference in sound is noticeable only with a large difference in the reproducible ranges (for example, 20-200 Hz and 50-150 Hz).
Also, do not forget that an extensive frequency range is not yet a guarantee of high-quality sound; and in some cases (for example, if the main speakers of the speaker also cope well with low frequencies), it may be completely redundant.
Crossover frequency
Cutoff frequency of the crossover installed in the subwoofer (or supplied with it — for passive models, see "Type").
The crossover splits the audio signal into separate frequencies so that only the bass goes to the subwoofer and only the main range goes to the speakers. Such a device is mainly equipped with home models (see above). And the crossover frequency is the upper threshold of the frequencies fed to the subwoofer. This information is important for matching with the rest of the speakers: ideally, the lower threshold of the main acoustics should correspond to the upper threshold of the subwoofer, otherwise the frequencies will either overlap or dip in them (neither of which contributes to sound quality). For the convenience of matching, the crossover can be made adjustable (see above).