Literal Translation
To have the arse on fire
Actual Meaning
Either: to be in a rush, or: to be really horny
Etymology
The first meaning dates back to the late 17th century.
The image is clear because we understand that someone whose backside is on fire will instinctively start running very fast in the foolish hope of putting distance between themselves and the fire, even if this is not necessarily the best possible reaction.
The second meaning appeared in the mid-16th century.
It is based on the idea of being (very) horny, but with the location of this “heat” being somewhat vague.
Obviously, this somewhat vulgar expression makes perfect sense in certain contexts, but it remains very informal and should be avoided in front of sensitive souls! There are still nicer ways to describe sexual desire, such as “la saison des amours” or “grimper au rideau”.