There is no bilateral healthcare provision agreement between the UK and Jordan, so travellers to the country need to ensure that they arrange comprehensive medical insurance prior to travel. Medical care in Amman is of a high standard - comparable with the UK and Europe, but away from the city in rural areas, you are more likely to be treated with leeches and potions than by modern anti biotics, and you are advised to carry a basic healthcare kit with you if you leave the capital. Treatment is quite expensive - almost every treatment needs to be paid for before it will be given and for some severe conditions you would have to be extracted from the country in order to receive treatment elsewhere, so you should ensure that any insurance includes provision for air ambulance within the policy.
Tap water is not always safe to drink, and you should stick to bottled water from a sealed container for your own protection while in the country.