[1] Colloquially, an image is burned when it contains uniform blobs of color, black, or white where there should actually be detail.
While converting and capturing images is usually a "smart" process that tries to accommodate the entire gamut of the original into the target color space, extreme processing of an image usually results in burning, as defined above.
A more subtle case of burning occurs when an image's saturation is increased too much.
In this case, avoiding the burn is much more difficult if the saturation needs to be increased to the respective level, because all other colors need to be adjusted proportionally, or discoloration will occur.
Typically, as a rule of thumb, shadows are more "forgiving" with burning than highlights.