It means they have applied and been accepted by one of the several professional bodies in the UK. All these bodies require a therapist to have completed his or her education at a respected educational establishment, and to have suitable experience. A registered therapist has also signed a contract agreeing to uphold the strict ethics of practice of their professional body.
In summary, a registered therapist is qualified and committed to providing good quality care. If they don’t, you can and should report them.
For more information, read our article on the Benefits of Working With a Registered Therapist.