A proprietorship usually means a sole proprietorship, a business owned and run by one individual that has not been set up as a separate legal entity such as a corporation or limited liability company (LLC). The owner receives all the profit and is personally liable for the business's debts. The main entry covers its features, taxation and accounting.
Other uses of the word
In law and everyday speech, "proprietorship" also means ownership in general, and a proprietor is the owner of a business such as a shop or hotel. "Proprietary" comes from the same root and describes something privately owned, such as proprietary software.
In older accounting textbooks, proprietorship was also used for what is now called owner's equity: the owner's claim on the business's assets after liabilities are deducted. The accounting equation was sometimes written as Assets = Liabilities + Proprietorship. The word has largely fallen out of use in that sense.
For a proprietorship as a business form, the owner's equity is kept in a single capital account, with withdrawals for personal use recorded in a drawing account. Although the business and the owner are the same person in law, the accounting records treat them separately under the economic entity assumption. When two or more people own an unincorporated business together, it becomes a partnership rather than a proprietorship.