Anytime ArcGIS handles a raster dataset that is stored on the file system, an .AUX file is created. An .AUX file is also created if the raster dataset is used with ArcObjects code, or browsed to in ArcGIS.
The .AUX file is stored on disk in the same location as the raster dataset. The exception to this rule is when the folder containing the raster dataset is read-only. In this case, the .AUX file is stored in the RasterProxies folder.
An AUX file tends to be small, however if they are created for thousands of raster datasets, they can potentially take up a large amount of disk space.
It should be noted that with ArcGIS 9.2 and beyond, an AUX.XML file may be created for some raster formats - for the same reason.