Legal person refers to a human or non-human entity that is treated as a person for limited legal purposes.
Typically, a legal persons can sue and be sued, own property, and enter into contracts.
"Legal person" is used frequently within the field of business law.
Laws dealing with business organizations (i.e. corporations, partnerships, limited liability companies, etc.) often use the term "legal person," so that the laws apply to humans, as well as non-human business entities.
"Legal person" has relevance in election law as well. In Citizens United v. Federal Election Commission, 558 U.S. 310 (2010), the Supreme Court upheld legal personhood for corporations which want to contribute to political campaigns.
For more on legal persons, see this Yale Law Journal article, this Wake Forest Law Review article, and this Penn State Journal of Law and International Affairs.