Why is AMBULANCE written backwards? So you can read it in your mirror
AMBULANCE is written backwards on the front of the vehicle so that a driver ahead can read it in the rear-view mirror. A mirror flips writing left to right. Lettering printed already flipped gets turned back the right way round, and the driver sees a plain AMBULANCE coming up behind them without having to decode anything.

What the mirror does
Hold a page of text up to a mirror and every word reads backwards, letters reversed and in reverse order. A rear-view mirror does the same to whatever is behind the car. If an ambulance carried normal lettering on its hood, a driver checking the mirror would see it reversed and have to work it out, in traffic, with a siren going.
Printing the word mirror-imaged solves that. The mirror reverses the reversed word and the driver reads AMBULANCE at a glance. It costs nothing, and it only has to work from one direction, because the front of the vehicle is the side that other drivers see in their mirrors.
It is written into the rules
In the United States this is not a styling choice. The federal specification for ambulances, KKK-A-1822, published by the General Services Administration, sets out exactly how the markings must look. The 2007 edition, KKK-A-1822F, says that on the front “the word ‘AMBULANCE,’ mirror imaged, shall be in block, blue, die cut style letters, not less than 4″ high, centered above the grille, on the orange or white background”. It allows the word to go on the curved surface of the hood or on a flat plastic bug screen, and requires a three-inch blue Star of Life, the six-armed emergency medical emblem, on each side of it.
The same specification treats the other sides differently, which shows the mirror logic at work. On the sides and rear, the word AMBULANCE appears the normal way round, in letters at least six inches high, because people see those sides directly rather than in a mirror. The roof carries a Star of Life at least 32 inches across. The 2007 edition replaced an earlier version dated June 2002, and the specification itself goes back to the early 1970s, although we could not open the original 1971 text to check whether the mirrored lettering was in it from the start.
The colours are fixed too
The specification is fussy about colour too. It sets the letters in blue on a white or orange background and defines the blue and orange by reference to an American safety colour standard. The effect is that every ambulance built to the rule looks alike. A driver does not need to read carefully when the shape, the colour and the word are ones they have seen hundreds of times.
Newer American ambulances are increasingly built to a different standard, NFPA 1917 from the National Fire Protection Association, which was modelled on the federal specification. We could not check its exact wording, because NFPA standards are sold rather than published free. The reason for the backwards word does not depend on the rulebook: the most important reader of the word on the hood is looking at it in a mirror.

