Depicted on tv, they were shown as people living in the higher dimensions in association with God. i.e. divine beings hardly seen by human beings. Their purpose, to follow the will of God which includes reaping souls, maintaining the peace via force and they are aided by the power of God in their work. Alongside the Shimigami are their Zanpakto, a living weapon usually seen in the form of a sword or swords and occasionally a staff. Each is specialized in various art forms such as energy manipulation, research & development and various fighting styles from thought the universe. In some cultures Shimigami we're known as archangels, apkalu or other beings who help God with energy, purifications, gathering knowledge and punishment of miscreants.
Sometimes the hand of God is felt directly when punishing miscreants, otherwise the Shimigami are sent.