This is a movement in some Pentecostal circles. It is an error in the understanding of the nature of the Trinity. The Biblical Trinity consists of three persons simultaneously and eternally existing in one God. The Jesus Only Movement maintains that there is only one person in the Godhead: Jesus. One view held in the Jesus only movement is that the person of the Father became the person of the Son who then became the person of the Holy Spirit and that the persons are consecutive not simultaneous. Another view is that the Father, Son, and Holy Spirit are not consecutive but are manifestations of the one person that occurs at different times and situations.
This movement is heretical. Additionally, they mistakenly believe that baptism is necessary for salvation and that tongues are evidence of true conversion. See the Plurality Study for an article that helps to refute the idea that the Father became the Son who became the Holy Spirit. Another term used to deny the Trinity is Oneness theology.