How did this come about?

The original Hebrew word is מַצָּה, pronounced as “matzoh” among Ashkenazi Jews and “matzah” by Sepharadic Jews (as well as speakers of Modern Hebrew).

Matzo reflects common Ashkenazi pronunciation (which dominated in English speaking countries in past centuries) but is not entirely accurate since it drops the “h” from the end.

Matzah, on the other hand, retains the “h” and can be read accurately and easily by both Ashkenazim and Sephardim.

Plural: Matzos, Matzoth, Matzot, or Matzahs

In the plural form, מַצָּה becomes מַצּוֹת. The final letter of this word (ת) is pronounced differently among different traditions. It appears that the accurate pronunciation, still retained among some Yemenite Jews, is “th.” Thus, matzoth would be technically accurate.

However, this does not reflect the way that the vast majority of Jews speak today. Living in countries where the “th” does not exist, Ashkenazim instead pronounce the ת as “s,” and Sephardim modified it to “t.” Thus matzot is proper for Sephardim and Modern Hebrew speakers, and matzos is proper in Ashkenazic parlance.

It is also perfectly acceptable to simply treat it as an English word and use matzahs for the plural.