Gethsemane is an urban garden at the foot of the Mount of Olives in Jerusalem. In Christianity, it is the place where Jesus underwent the agony in the garden, and where Judas betrayed Jesus.
Gethsemane appears in the Greek original of the Gospel of Matthew[1] and the Gospel of Mark
According to the New Testament it was a place that Jesus and his disciples customarily visited, which allowed Judas to find him on the night of his arrest.
Source: Wikipedia
All of the foregoing is based on long-held tradition and the conflating of the synoptic accounts of Mark (14:31) and Matthew (26:36) with the Johannine account (John 18:1). Mark and Matthew record that Jesus went to “a place called the oil press (Gethsemane)” and John states he went to a garden near the Kidron Valley.
Source: Wikipedia