The Greek word charisma (Strong's Concordance #G5486), from which we derive the modern word Charismatic, is translated in the King James Version Bible and New King James Version Translation as 'gifts' (Romans 11:29, 12:6, 1Corinthians 12:4, 9, 12:28, 30 - 31). In general, it can be stated that anyone who is a true Christian and who exercises one of the many gifts that God's Spirit can give is charismatic.
The apostle Paul used charisma in 1Corinthians 12 to designate the supernatural gifts made available to individuals through the power of the Holy Spirit. These are many times referenced as the charismatic gifts of Christianity.
In the middle of the 20th century a new variation of Christianity arose, called the charismatic movement, which emphasized practicing 'visible' gifts (speaking in tongues, healings, etc.). It also focused on a 'baptism of the Spirit' as an identifying sign of conversion. Although it started in mainline Protestant churches, the charismatic movement soon spread to others such as the Catholic Church. In recent times, many leaders in the Charismatic movement have been convinced that the manifestation of supernatural power (for example, alleged healings, delivering a person from the influence of demons, tongues speaking, etc.) can and must be an integral part of their evangelistic efforts.
7. But the manifestation of the Spirit is given to each one for the benefit of all. 8. For to one, a word of wisdom . . . knowledge . . . faith . . . healing . . . miracles . . . prophecy . . . and to a different one, various languages . . . 11. But the one and the same Spirit is operating in all these things, dividing separately to each one as God Himself desires (1Corinthians 12)
When applied to religious-related groups like churches or teachers the word Charismatic generally implies that those involved believe all New Testament gifts (1Corinthians 12, Romans 12, etc.) are available today to believers.
Additionally, they believe each Christian should expect to experience one or more of them on a regular basis, including such manifestations as tongues speaking and healing. This term is also applied in secular settings to indicate a non-spiritual quality of strong personal appeal and powers of persuasion (such as a politician or public speaker).