To bring all levels of a multi-layered image down to one plane.  High-end graphics programs provide a multi-layer file format, such as the Photoshop Document (PSD), which enables elements in each layer to be manipulated independently.  In order to save the layered image in a single-layer graphics format such as TIFF or JPEG, the image is said to be "flattened."
An Adobe PDF file is also flattened to remove a transparency layer when the document is rendered in a printer or in an application that does not support the additional layer.  See 
layers and 
PSD.