The White Stag was a male deer whose origins and whereabouts are steeped in mystery. According to legend, whoever caught the beast would have their wishes granted.
Well over a year after the Archenland Conflict, High King Peter, Queen Susan, King Edmund and Queen Lucy were told about the mythical beast by Mr.Tumnus. He said that it had "Once more appeared in his parts", indicating the Stag had been to Narnia before.
They hunted the stag in Lantern Waste, near the Lamp-post, in order for the empire to have its wishes granted. However, they were unable to catch it, and instead unintentionally returned to Earth through Digory Kirke's Wardrobe, through which they reverted back into children, thus un-fulfilling their wishes.
It's been theorized that the Stag was really Aslan in disguise, guiding them back to their world, as they had done all that they needed to do.