John Wesley was a priest in the Anglican Church, a Protestant denomination.
Methodism is a method of trying to live as Jesus Christ said people should live. Prior to John Wesley, European Christianity was pretty much an elitest religion for "the privileged". Many clergy felt that the "lower classes" were incapable of living a moral life, and felt it was beneath them [the clergy] to go into bars, pool halls, gambling halls, hospitals, etc., to try and tell "those people" about Jesus.
John Wesley lived most of the 18th Century. Along with his brother Charles, who wrote several thousand hymns, and a few of his friends from seminary, he started Methodism. The term 'methodist' began as a derogatory term used by several of his classmates because his group took a methodical approach to studying scripture, ordering their daily activities, etc. The Wesleys began going to "the dregs of society" and preaching about salvation and moral living, and helped lead many to salvation.
Methodism was a leader in opposing slavery in the United States and also in the civil rights movement in the mid-20th Century, and several Methodist sub-denominations in the United States are predominantly black memberships, e.g., Christian Methodist Episcopal (CME), African Methodist Episcopal (AME) and African Methodist Episcopal Zion (AMEZ). (Episcopal refers to heirarchy, i.e., the denomination has bishops who oversee numerous churches, each with a pastor.)
Sadly, in recent years the largest Methodist denomination in America, United Methodist, has begun to drift from mainstream Methodist doctrine. If you hear some report about a "Methodist" doctrine which you feel is unbiblical, before condemning the "Methodist position" please check whether other Methodist denominations agree with that position!
More about Methodism.