The term "check-the-box regulations" refers to treasury regulations that allow partnerships (any entity not classified as a corporation) to elect to be taxed as partnerships under Subchapter K or as corporations under Subchapter C. These regulations, contained in Treas. Reg. § 301.7701-3, simplified the prior "corporate resemblance" six-factor test that was used to determine whether unincorporated entities would be classified as corporations for federal tax purposes.
Under the regulations, an unincorporated entity with two or more partners can elect to be treated as a corporation or a partnership. An unincorporated entity with one owner can elect to be treated as a corporation or as a "disregarded" entity. In either case, the election to be treated as a partnership (which occurs by default if no election is made) avoids the double taxation of Subchapter C.
An exception to this general rule is that "publicly traded" partnerships under Section 7704 of the Internal Revenue Code will be treated as corporations.