It's a "broad hatchet." Used for shaping by carpenters and ship builders, chair makers, etc. Plumb started making broad hatchets in partnership in the 1860's, and owned the company in 1887. I had one from my great grandfather, and he was a cement contractor in the early 1900's, so I expect he used it for making concrete forms. I might still have it someplace in the shop. Some were made with a sharp bevel only on one side, others were beveled on both sides of the blade, so that they were a center cut.
A broad hatchet is beveled and sharpened on both sides and used to cut and split wood, a hewing hatchet is only beveled and sharpened on one side, either left or right and used to hew, straighten, shape and smooth wood as mentioned by Bosnmate.
Without any maker's marks it would be hard to determine the age of the one you have, other than the apparent age of the corrosion, that style is still made today.
If you do electrolysis on the hatchet you may or may not find maker's marks.