That was a mouthful! More commonly known as pigeon pose. So I'll break down the sanskrit name for you: eka means one, pada is foot or leg. Kapota is a dove or pigeon. Rajakapota means the king of pigeons. In this asana, the chest is pushed forward like that of a pouter pigeon, hence the name of the pose.
There are many variations of this pose and I can't do some of them. But there are certain effects to practicing this cycle of asanas. According to "Light on Yoga" eka pada rajakspotasana is rejuvenating the lumbar and dorsal regions of the spine. The neck and shoulder muscles are fully exercised and the carious positions of the legs strengthen the thighs and ankles. The thyroids, parathyroids, adrenals and gonads receive a rich supply of blood and function properly, which increases vitality. In these poses more blood circulates the round pubic region, which is kept healthy. This series is recommended for disorders of the urinary system.
Not to mention one hell of a hip opener!
Be safe and mindful when practicing this asana and its many variations. Watch the knees and lower back. Be sure to use props underneath the hip and knee if they don't sit comfortably on the ground.