In general, an association is a group of persons banded together for a specific purpose. To qualify under section 501(a) of the Code, the association must have a written document, such as articles of association, showing its creation. At least two persons must sign the document, which must be dated.
The definition of an association can vary under state law. You may wish to consult the law of the state in which the organization is organized. Note that for an association to qualify under section 501(c)(3) of the Code, its articles of association must contain certain language. Publication 557 contains suggested language.