On Thursday of Holy Week the Church remembers Christ’s Last Supper with his apostles and sets the scene for what will happen the next day. During the the celebration of the Lord’s Supper, the liturgy re-enacts in a solemn way the movement of Jesus to the Garden of Gethsemane.
After the distribution of Holy Communion the priest does not place the remaining hosts in the primary tabernacle where the Blessed Sacrament is usually reserved. Instead he places them on the altar.
The Roman Missal then continues the description of what happens next.
A procession is formed in which the Blessed Sacrament, accompanied by torches and incense, is carried through the church to a place of repose prepared in a part of the church or in a chapel suitably decorated…When the procession reaches the place of repose, the Priest, with the help of the Deacon if necessary, places the ciborium in the tabernacle, the door of which remains open. Then he puts incense in the thurible and, kneeling, incenses the Blessed Sacrament, while Tantum ergo Sacramentum or another Eucharistic chant is sung. Then the Deacon or the Priest himself places the Sacrament in the tabernacle and closes the door.
Often the Eucharist is placed in a secondary tabernacle on a side altar, or in an area of the church that is most suitable. This procession from the main altar to another location in the church is symbolic of the movement of Jesus to the Garden of Gethsemane, where he experiences great agony before his arrest and betrayal.
Read more at Aleteia.