My house sheathing is not a plywood - but some dark brown material.
Does anyone know what that is?
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It was made by Celotex as well as some other companies. It comes under the nickname Buffalo board and Beaver board depending on where you're at. I don't know that it's manufactured anymore, however I viewed the link from the previous answer and it appears it could be the same thing.
If your house is older then it is probably the original buffalo board material. If it is newer it could very well be the exact same thing that is sold at Home Depot mentioned in the link that was provided in the first answer.
The generic name is "fiberboard" and it is sold under many trade names like Celotex, Buffaloboard, etc. This stuff is not bad at all, it's just different from plywood and OSB. While plywood and OSB are structural and offer substantial racking resistance against wind load, fiberboard is weaker and does not increase the strength as much. On the plus side, it is basically impervious to moisture due to the chemical additives, so it will never rot or grow mold. It is also highly vapor-permeable, enhancing drying to the exterior should the wall get wet. Also, it is a reasonable insulator, around R-3 per inch. So half-inch fiberboard adds R-1.5 to your whole house. Not bad. Finally, I can tell you from personal experience that termites don't like it. They'll eat wood all around it but won't touch it.
This looks like what we call "asphalt board", a kind of impregnated wood fiber board. Example
Looks like Masonite® to me. The product was "slick" on one side ("finished") and "fuzzy" on the other. Commonly used as "pegboard".