A British word meaning flimsy or bendy, used to describe large pieces of material like metal or wood. It can also be used for food like cake that has become soggy and floppy (so that it dips in the middle).
It comes from the sound made when large sheets of metal are shaken, so that parts of the sheet turn inside out and make a strange wobbly noise.
1. Be careful carrying drinks on that large tray; it's very wappy.
2. I added too much water to my cake, and now it's gone a bit wappy.