The sound ‘Jaya’ is uttered both at the beginning and at the end of Puja to signify praying of Grace of Guru- Vaishnav-Bhagawan.
The word ‘Jaya’ literally indicates to the conquer.
May Guru-Visahnav-Bhagwan conquer me – make me their own – grace me – bestow me their service.
For devotional performance Grace of Guru – Vaishnav – Bhagawan is essential.
— His Divine Grace Srila Bhakti Ballabh Tirtha Goswami Maharaj.
Source: http://www.bvml.org/SBBTM/jaan.html