The Greek verb haptomai (middle voice of haptō) means to touch, to take hold of, to handle, to fasten oneself to. Haptō in active voice means to fasten or kindle (a fire). In the NT the middle voice — personal, intentional touching — is overwhelmingly most common, especially in healing contexts.
The theology of haptomai in the Gospels is extraordinary. The ritually unclean — the leper, the woman with the flow of blood, the dead child — are not to be touched; touching them transferred defilement. Jesus reverses this: when He touches the leper (Matthew 8:3), He does not become unclean — the leper becomes clean. When the woman with the hemorrhage secretly touches Jesus' garment (Mark 5:27-34), power flows out from Him. His holiness was more contagious than their uncleanness. John 20:17's 'Do not touch me' (mē mou haptou) — better translated 'Do not cling to me' — speaks to Mary Magdalene's need to release the earthly intimacy for the coming new mode of Christ's presence through the Spirit.