Distance and aircraft type
The biggest driver. Longer sectors need larger, longer-range aircraft, and may require fuel stops that add hours, landing fees and crew time. A short regional transfer and an intercontinental repatriation are different orders of magnitude.
Medical crew and equipment
A nurse-and-paramedic team costs less than a doctor-led critical care team. Ventilation, infusion pumps, specialist monitoring, neonatal equipment or additional oxygen all add to the configuration and therefore the price.
Ground transport at both ends
Ambulances from the ward to the airport and from the airport to the receiving hospital are part of the mission. In some countries these are inexpensive; in others they are not.
Permits, handling, slots and airport hours
International flights need overflight and landing permits, ground handling and sometimes customs and immigration attendance. Airports with restricted hours can force an overnight, which adds crew accommodation and duty-time cost.
Timing
An immediate departure costs more than a planned one, because it uses whichever suitable aircraft and crew can be positioned now rather than the most efficient option.
How to get a number you can rely on
Give the provider the patient's location and treating facility, a current medical summary, the intended destination, and who is paying. A quote based on that will hold. A quote given without it will move.