Within a Jewish community, the Bet Din will deal with matters of a specific Jewish nature. There is separate Bet Din for each of the main branches of Judaism in the UK, such as the orthodox and reform traditions. As far as the personal lifestyle of a Jew is concerned the Bet Din deal with matters that include providing kosher certification, resolving civil disputes and making judgements on medical ethics.
The Bet Din acts as an arbitrator when there are civil disputes over matters such as property or business disputes. In the UK the Bet Dins arbitration in such disputes is recognised by the arbitration act and is therefore legally binding also the Bet Din may be called upon to assist Jewish patients and their relatives with any questions, which may arise related to medical ethics. These questions could be related to treatment or end of life issues such as abortion and euthanasia. The decisions related to medical ethics will depend very much on the branch of Judaism to which the bet din belongs.
The Beit Din is part of a Jewish community, enforcing its laws and strictures and protecting its members. It's like asking "How does an American Courthouse help support the American way of life?"