There is probably a thread about this somewhere, so type in Cued Speech in the search area and you will probably find something much better than this. There are also people who know way more about this who will hopefully respond, like loml, hopefully.
But, to give you my abbreviated version, trying to be as objective as possible:
Cued speech is used by deaf/hoh people to aid lipreading. Some sounds look EXACTLY the same on the lips, so, to differentiate, handshapes have been made that correlate with certain sounds. That way, when people aren't sure if you are saying, for example, "ma" "pa" or "ba" they can see your handshape and know. Essentially, cued speech makes some phonetics visual.
This system is much easier for adults who have lost their hearing, and hearing people working with deaf children to learn than a signing system or language.