With an Infant Mortality Rate at 86/1000, Nigeria is ranked lower than war-ravaged countries like Iraq and Congo DR.
The Infant Mortality rate can be used as an economic indicator, just as much as it tells how good the healthcare system is.
Succinctly put, there are about 200 countries in the world that are 'richer' and have a better health care system than Nigeria.

Many reasons can be implicated for this, but from my experience, the single most important reason is the government, who have been trying to 'climb the tree from the top'.
I am referring to the excess funding of teaching hospitals as compared to primary health care centers.
Dr Olikoye Ransome-Kuti (the best minister of health Nigeria ever had), started the drive of primary health care centers, but this was killed by successive administrations. I remember how much he advertised Oral Rehydration Solution (ORS) for dehydration, which remains the number one killer of infants.
If government provided a decent primary health care center in each community, a trader living in Ojuelegba, for example, will not go to Unilag teaching Hospital for her malaria treatment.
Tertiary health centers could then serve as referral centers, for cases that cannot be treated by primary care or secondary care centers.

Other problems with the healthcare system include:

-Staffing: The spate of exodus of doctors in Nigeria is alarming. The solution shouldn't be geared towards increasing doctors' basic salaries alone, but rather to increase benefits such as Hazards allowance, loans etc, and more importantly, improve the tools doctors work with. It is not that doctors in the US, UK or India are better than doctors in Nigeria, but they have better tools to work with, i.e much better laboratories, diagnostic and therapeutic equipment. I think it is even more difficult to get into medical school in Nigeria than in the US.

- Accreditation: It is hard to tell which private clinic is manned by a doctor, registered nurse, auxiliary nurse, or even mechanic in Lagos. Stricter controls should be placed on private clinics.

- Drugs: Dr Akunyili, during her time as NAFDAC boss once stated that about 60% of drugs in Nigeria were fake or substandard. This means it was/is more likely to buy fake or substandard medications than legit ones.

-Access to drugs: Every Uzo, Tunde and Nasir can walk into a pharmacy to buy Ciprofloxacin or any other antibiotic. The problem this causes is that more resistant bacteria strains develop and infections are harder to treat. A common scenario that plays out is a patient comes to the hospital for an infection and the doctor prescribes a medication, but the patient tells him "Oh, I just used this for 5 days, it didn`t work". And they go on and on,

-Education: This is a major problem, and it is compounded by the fact that anecdotal evidence is the first resource many Nigerians seek on health matters. Many people end up with traditional healers who claim they have the cure to all ailments. I have actually seen pastors claiming to cure HIV by prayer!! Many times, these patients end up the worse for it. I remember a patient I encountered while in med school. He was hit by a car, and was given 40,000 naira to fix his broken leg. He visited a traditional healer who charged about 5,000 naira. Well, he came to the Hospital 2 weeks later with gangrene of the leg, and had to have an amputation to save his life.

-Social services: Water, electricity, good roads, etc are basic social services that improve the standards of living of the people. Provision of these would automatically improve the state of health of the people. A universal health care insurance should also be put in place. The current National Health Insurance Scheme is simply not working, just like any other government project in Nigeria.

-Attitude: In Nigeria, the death of a person is as trivial as weekend news. No one really cares. The government will not be moved to build better roads because of car accidents, or better equip hospitals because of increased mortality. They do not care. Since Nigerians have a high fertility rate, we can always replace the lost ones :-)

Finally, a prayer for Nigeria: May God bless the hearts of the common man, to elect a leader that would eradicate corruption.