Betel nut is an important item in most Hindu Pujas. Some communities establish the murti of Ganesha and Goddess Gauri in Betel nut. The belief is that Betel is a complete fruit and is pure. In South India, betel leaf and betel nut is a must for giving Dakshina to Guru and elders.
In some regions, holy thread is also offered to betel nut.
Some people also keep betel nut inside the vault where money, gold and property documents are stored.
In olden days, betel nut was considered very pure as it had a natural coating. In North India, this natural coating was removed in the presence of the murti and offered as a pure offering. The ritual is still followed but sadly most often we end up offering unclean ones or reused ones.
In South India, the offering is always made without removing the outer covering of the betel nut. It is an important item during marriages, housewarming etc.