The most common definition of a partnership is that from Section 6 of the Uniform Partnership Act: "An association of two or more persons to carry on as co-owners a business for profit." Each part of the definition is important.
The partnership must be an association of two or more persons. So in contrast to a corporation or a limited liability company, there is no concept of a general partnership wholly owned by one person.
Second, the two or more persons must carry on as "co-owners." Thus, if one person hires another person to work as an employee without giving the employee any ownership interest, they have not formed a partnership but rather an employment relationship.
The partners must associate to carry on a business for a profit. Thus, again in contrast to corporations (and possibly LLCs), there is no concept of a charitable partnership.
Note that the definition does not include a requirement that the partners intend to enter into a partnership relationship. A general partnership can be formed when the requirements are met, whether or not the partners intended to enter into a general partnership.
The default rule in general partnerships is that each partner has equal rights to manage the partnership. This structure can be varied in the partnership agreement, however.
The general partnership is taxed as a partnership, meaning that it receives pass-through taxation treatment. The partnership itself does not pay an entity-level tax; instead profits and losses are passed through to the individual returns of the partners.
Entity Theory Versus Aggregation Theory
A recurring question in partnership law over the decades is whether the partnership is an entity separate from its partners like a corporation (the "entity theory") or merely an aggregation of individuals (the "aggregate theory"). The UPA took an entity perspective on some issues such as property ownership, but not on others. The RUPA expressly affirms that the partnership is an entity in line with more modern case law.