Why do jet engine igniters require huge voltages?
In short, 40 kV isn't that much voltage for applications that are intentionally creating an electrical arc. Car spark plugs also use voltages in the tens of thousands of volts for the same reason, for example.
As for why that is:
In general, air acts as an electrical insulator. That is, electricity won't pass through air at normal voltages. Which is good because otherwise you'd have a constant arc to ground through the air from any exposed hot conductor and that would cause lots of problems.
As with any insulator, air has a dielectric strength, measured in volts per unit distance. For a given length of air (such as the spark gap in a spark plug,) there exists a breakdown voltage at which point the voltage differential per unit distance exceeds the dielectric strength. When a voltage equal to or greater than the breakdown voltage is applied to conductors on either side of said length of air, the air will suddenly ionize, creating a channel of plasma through the air. The plasma channel now has a much, much, much lower resistance than air normally has, allowing current to flow across the gap and quickly equalizing the potential (i.e. voltage) on each side of the gap.
As you're likely aware, plasma tends to be quite hot. The plasma channel created by the above process is the visible arc that you'll see between the conductors in a spark plug.
For air at normal pressures, the dielectric strength is about 3 MV/m. That is, if you want to create a 1-meter arc, you'd need 3 megavolts of potential across it. Or, in units more suited to creating ignition sparks (which are hopefully not a meter in length,) you need around 3 kV per millimeter. So, for example, in the winter when you take off a fleece coat and then experience a shock the next time you get close to a grounded conductor, the static potential that has built up on you is about 3 kV per millimeter (i.e. 30 kV/cm or around 75 kV/inch) of the maximum length of the arc you can create to such a conductor.
So, in summary, 40 kV really isn't all that much when you're trying to create arcs through air, especially not highly pressurized air, such as in a piston or jet engine. Even relatively small distances require quite high voltages in order to arc. Which is a good thing so that exposed conductors don't just constantly create arcs to ground. Or to grounded people, electronics, etc.
By the way, this ability of an electric field to ionize air is why switches for very high voltage transmission lines have to have much, much longer poles than what you'll find on normal switches. On a 138 kV line, for example, the electricity would simply arc across a switch that created a gap of less than couple of inches or so when open. Perhaps an even larger gap when humidity is high. And these switches do indeed arc while opening and closing. They can also create quite long arcs while opening, since the plasma channel is already in place. Here's an example of what that can look like at 138 kV:

                
            
Of course, in this case, you have a more-or-less continuous voltage source, not just a stored-up charge that is suddenly released, so the arc won't just be a brief flash, but will continue until the distance between the conductors becomes too high to maintain the arc.
And, of course, when the potential between the base of a cloud and the ground gets too high, you get lightning. And, yes, that's a very, very high voltage to arc across a kilometer or more. According to the U.S. National Weather Service, a typical lightning bolt involves potentials of around 300 MV. While that actually seems a bit low to arc across the typical distance of a lightning bolt, lightning normally occurs in thunderstorms where the atmosphere is already very humid and, thus, more conductive than normal.

As far as the ease of igniting jet fuel, while that's mostly unrelated to the voltage required to create a spark across a given distance of air, it's actually not that easy to ignite. At standard air pressure, you can drop a lit match in a bucket of jet fuel and it will just extinguish the match. You can also create a raging fire in the fuselage of a Boeing 777 and the fuel remaining in the tanks of said 777 won't burn. This is by design and it's one of the great things about jet fuel for aviation. While the energy density and specific energy of petroleum fuels is very high (by chemical reaction standards,) it actually requires quite high temperatures and/or pressures to ignite jet fuel, making it an ideal fuel for providing lots of energy per unit weight while not tending to randomly burn or explode at inconvenient times.