The broadest definition of this term is a God who is a personal being, i.e. a being with a personality, including the capacity to reason and feel love, as in the cases of Zeus, Apollo and Athena and other deities common to European Pagan polytheism. In the case of the Christian belief in the Trinity, God is an impersonal 'ousia' or substance, manifested in three 'hypostasis' or persons, the Father, the Son, and the Holy Spirit. These views are intended to challenge the concept of deity which is merely a guiding principle, a blind creative force or a philosophical ideal.
A narrower interpretation of a personal God is a deity who takes a personal interest in the world in general and worshippers in particular. This view is intended to challenge a deistic outlook.
A still narrower definition would be a God whose personal interest in His worshippers is so great that the deity communicates directly with them and actively intervenes in their lives through miracles.
The most restrictive interpretation of a personal God is a deity that is solely concerned with his worshippers, having pity at best and animosity at worst towards non-believers. Jehovah, the jealous God of the Torah, was the personal God of the Jews. Most modern denominations believe that they have the clearest understanding of what God wants, but some modern fundamentalists suggest that those who are not members of their church will experience damnation.