A health certificate is a certificate of veterinary inspection where the signing veterinarian endorses that your pet is healthy and free of any transmittable diseases.
When traveling between states within the continental United States a health certificate needs to be issued within 10 days of travel and must be accompanied by an exam by your veterinarian.
When traveling outside of the continental United States please contact the hospital as soon as possible in order to inquire on the requirements for your destination. Many countries have very specific requirements that can take a month or more to complete.