Persons, churches, movements, etc., affirming the belief that speaking in tongues is a gift of the Holy Spirit that may and should be manifested in the church today. These persons, churches, and movements are generally part of institutions and denominations that did not originate out of the original Pentecostal movement.
Definition from: "A Biblical Guide To Orthodoxy And Heresy Part One: The Case For Doctrinal Discernment" (an article from the Christian Research Journal, Summer 1990, page 28) by Robert M. Bowman.
Many charismatic churches, movements and proponents are controversial because of an overemphasis on the spiritual gifts, and not enough emphasis (if any) on the practice of Biblical discernment.
In a secular sense, charismatic refers to a person's charm or appeal, as in his or her ability (gift) to promote loyalty or enthusiasm (e.g. "a charismatic leader."). This is true even in a religious context. For example, a pastor can be a charismatic leader even if he is a cessationist.
Dictionary of Pentecostal and Charismatic Movements by Stanley M. Burgess (Editor), Gary B. McGee (Editor), Patrick H. Alexander. Avoids apologetics and polemical approaches, and focuses mostly on North America.