Tenerife is a Spanish territory and therefore all passport and residency rules are the same as on the Spanish mainland.
European Union citizens can travel to Tenerife with national ID cards alone. If your country does not issue identity cards, then a valid passport is required. All non-EU nationals require a full valid passport.
Keep your passport and other important documents safe at all times, perhaps lock them away in the secure box, which is supplied by your hotel. However, remember that you will need your passport or other photo ID documents, like a driving licence, if you are paying by credit or debit card or hiring a car for instance.
Nationals of the EU as well as Norway and Iceland do not require a Visa for a stay of up to 90 days. If you wish to stay longer than 90 days you will need to apply for a Residency Permit during the first month of your stay.
You do not require any vaccinations to visit the Canary Islands, unless you are coming from an infected area. Make a point of checking with your tour operator or local Spanish Embassy if in any doubt.
EU citizens can obtain a refund of most medical costs by using form EHIC, which are available from post offices, health or social security offices in your country.