A discretionary trust is a legally recognized entity. Trusts are a concept of Western law and not every legal jurisdiction recognizes them. In practise, a Trust is the registered/legal owner of an asset(s) and the beneficial owner(s) is someone else. The Trust Settlement (the document that brings the Trust into being) sets out the entitlement of the beneficiaries.
Trusts can be used for a variety of purposes. For example, in the context of business a Trust can hold the legal title to the company carrying on business (via ownership of the shares in the company). The Trust Settlement then provides that others are the beneficial owners.
In the case of a discretionary trust, it is often left up to the Trustee to declare who is the beneficial owner. Why so much discretion to the Trustee? Simply put, for tax planning.