Om Jai Jagdish Hare is the aarti most widely sung in northern Indian households, performed at the close of puja while a lamp is circled before the image of the deity.
An aarti is not primarily a song of petition. The lamp is offered, moved in a circle, and the verses accompany that offering; the singing and the light are one act. Because it closes the ritual, an aarti is usually the part of household worship that everyone present joins, including those who do not follow the rest.
The composition is attributed to Pandit Shardha Ram Phillauri, who wrote it in the 1870s in Punjab. It addresses Jagdish, the lord of the universe, a name of Vishnu, and its verses ask for the removal of sorrow and the steadying of the mind, acknowledging throughout that the devotee comes without merit.
Although written for Vishnu, it is in practice sung before many deities, with the closing lines adapted to whichever is being worshipped. That flexibility is one reason it travelled so far beyond its original setting, and it is heard at Diwali, at Janmashtami, and at ordinary evening puja.