There's a wonderful non-profit healthcare clinic very close to the hostel, Clinica Esperanza, which is very inexpensive (it's sustained through donations, and is registered as a non-profit in the States if you'd like to offer any support, and donations of supplies are also welcome, if you're coming down and have room in your bags). It operates kind of like a walk-in clinic, and is open from Monday to Friday, from about 7am to 6pm. This is a good place to go if you have something that's not dire that you need to see a doctor about (ie. fever, nausea, severe reaction to bug bites, a cut etc). Also, if you want your teeth cleaned or have a cavity, they have a dentist (stop by the clinic to check on hours for dentistry), which is also very inexpensive. The clinic has medication which they distribute when you see the doctor (included in the pricing), they don't have a separate pharmacy for just purchasing medication.
If you just need a pharmacy (for cough and cold medical, stomach problems etc), there's a small one located at Anthony's Key, where there is also a doctor's office and a recompression chamber for dive accidents, as well as an x-ray machine. There are several more pharmacies located in Coxen Hole. Most medication does not require a prescription (including medications that need a prescription in other parts of the world, like antibiotics or birth control pills).
If there is a severe medical problem, the public hospital is located in Coxen Hole, and depending on the problem, sometimes it is necessary for a patient to be sent to the mainland. The public hospital does not look like hospitals in North America, and facilities are lacking, however the doctors are well-trained. Getting flown to the mainland is at the patient's expense, and many of the hospitals on the mainland are private, so these are scenarios where insurance will really help. The medical costs in Honduras are no-where near what they are in the States, but they can still accumulate in a hurry if it's something severe.