When you take one cart out and put another one in.
For example if you had two R4i Golds, and one was "bricked" (broken, "as useful as a brick") by a failed update (for example turning the power off in the middle of the update)... you could start the update file on the working cart, and then when it tells you to press A to start the update, take the working cart out, put the broken cart in, and then press A, and the update will be applied to the broken cart, fixing it.
However the DSi and 3DS won't let you cart-swap (as they will not initialize a second cart in the middle of a "game"), which is why there's two update files.