A.  A Trust is a legal entity that is formed under an agreement between one person (the Settlor or Grantor); the terms of the trust transfers to another person (the Trustee), an asset; in this case an aircraft to hold on certain terms. In the case of an Owner Trust, the aircraft is typically held for one beneficiary, which is the Settlor.
In the case of a foreign owner of the aircraft desiring US registration, a Trust is required for compliance with the with FAA regulations because an owner can ultimately control the aircraft through their US Trustee (US citizen), who is the registered Trustee of the US registered aircraft.
Owner Trust - If a foreign person or company settles the aircraft in trust with a US Trustee, it may be beneficially owned.