The best way I have heard it described (in my opinion) is by Tertullian who uses the legal terminology of his day. In legal terminology you have only two things, persons and property. In his language he called them personae and substancia. The Father, Son, and Holy Spirit are three distinct persons (personae), who jointly and equally share the same property (substance). That substance is divinity itself. Each person is equally divine, although in the economy of the trinity (how the trinity is expressed in the carrying out of the plan of redemption) each person fulfills a different, but overlapping role with the other persons of the Trinity.
Picture the Trinity as like a business owned and operated by three equal share owners. One of the owners might run the day to day operations. Another might run the sales portion of the business. And still another might handle logistics or some other facet of the business. All metaphors break down, but I figure this captures both the distinctness of the persons as well as the unity they share.
