Demigod worship is generally frowned upon by Vaishnavas, those who are worshipers of Lord Vishnu or Krishna. According to Vedic teachings, the purpose of human life is to develop a love for God, so any other discipline or religious practice outside of loving God is seen as second class.
The demigods, referred to as devas, are the chief deputies of the Supreme Lord Krishna. Just as a president or prime minister has assistants and cabinet secretaries, Krishna also has assigned posts for elevated living entities to manage the affairs of the material world. Their duty is to see to it that things are running smoothly and also to grant benedictions to those who please them. There are thousands of devas, they each provide different material benedictions to those who worship them properly and vigilantly.
Generally speaking, those who are less intelligent worship the demigods. The reason they are considered less intelligent is because the demigods, by rule, are only allowed to bestow material benedictions. If one is seeking great wealth, success in material endeavors, or the acquisition of great powers, they approach one of the various devas. Lord Krishna Himself describes this in the Bhagavad-gita: “Men of small intelligence worship the demigods, and their fruits are limited and temporary. Those who worship the demigods go to the planets of the demigods, but My devotees ultimately reach My supreme planet.” (Bg 7.23)