Curved needles are used when you need to hand-sew something where you cannot get to both sides of the piece. The curve of your needle allows it to come out just after it goes in. I initially saw it used to sew up the seams under chair arms after the upholstery is almost complete.
John James makes curved needles with a tapestry point.
A YouTube video from Starke Art shows how to use a curved needle when finishing needlepoint. It’s part of their series on needlepoint finishing.,