A chine appliqué print (also called a chine collé print) is a print where the image has been impressed onto a thin sheet of China paper (or other thin paper) and then that thin sheet is backed by a strong, thicker sheet of paper. These are fairly easy to spot: often the backing paper will age to a different color than the China paper, but even if not when you look closely at a chine appliqué print you can see the edge of the China sheet (usually just beyond the edge of the printed image).
Chine appliqué prints were made a fair bit in the nineteenth century for a number of different types of images. The reason this was done is because the thin China paper takes an intaglio impression more easily than a thicker sheet of paper, so that that chine appliqué often has a richer appearance than a standard print. This was sometimes done for proof prints (cf. blog on proof prints).
To this extent a chine appliqué print is often more desirable than a standard print, however there are several possible problems associated with these prints. First, the quality of the backing sheet is often not as good as that of a standard print, so this will sometimes discolor significantly more than the China paper, giving the print a somewhat distracting appearance. More importantly, however, is that a chine appliqué print is much more difficult to restore than a standard print. Any sort of immersion into water (which is often used in restoration) can lift the China paper off the backing and it is so thin that it can be difficult to reattach to the backing neatly. Chine appliqué prints can be restored, but only by a skilled conservator and there is definitely always the risk that the restoration will come out well. This doesn't mean one shouldn't buy a chine appliqué print with condition issues, but one must be aware of the risks.