In colonial times, the wealthier people had homes with stone floors. In winter, these slick floors became slippery, with muddy shoes and melted snow. To absorb the muck, homeowners spread thresh — or straw — onto the floor at the entry. This thresh would pile up and then spill out the door. To keep it in, homeowners installed a board in front of the door to hold the thresh. SOme say the this threshold eventually evolved to become today’s modern door sill that sits under the door, while the name stuck as the “threshold.”
Still others say that the board was put on the outside of the door, not to keep thresh in, but to keep barnyard debris out. I like the first story better, since it goes onto explain why folks that did not have stone floors were called, “dirt poor.”
Image: By Infrogmation of New Orleans – Photo by Infrogmation of New Orleans, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=18071782