What is the difference between a one way speaker, a two way and three way speaker?

The One-way Speaker or A subwoofer is a "low", as it plays only low frequencies. It is a one way speaker. A subwoofer is a woofer driver used only for the lowest-pitched part of the audio spectrum: typically below 200 Hz for consumer systems, below 100 Hz for professional live sound, and below 80 Hz in THX-approved systems. Because the intended range of frequencies is limited, subwoofer system design is usually simpler in many respects than for conventional loudspeakers, often consisting of a single driver enclosed in a suitable box or enclosure. Since sound in this frequency range can easily bend around corners by diffraction, the speaker aperture does not have to face the audience, and subwoofers can be mounted in the bottom of the enclosure, facing the floor.

The Two-way speaker have a main driver that covers low end to upper mid-range, and a treble driver.

The two way speaker design divides the frequency output of the amplifier sending the small wave part to the small tweeter and opposite larger wave part to the woofer. In three way speaker design there are two divisions. Three way design channels the medium size sound waves into a medium size or mid-range transducer. There are also four way designs that further divide the frequency spectrum bringing the reproduction of sound waves to drivers closer to the size of the wave that they are responsible to create.

The Three-way-speaker has at least three speaker elements with a crossover filter that directs low frequencies to the woofer, mid range frequencies to the mid range driver and high frequencies to the tweeter. A tweeter, mid-range, and woofer.