A curve following the inner side of a sphere. The enclosing side. The chair seat is essentially concave in principle as it’s enveloping and protective.
Perhaps the idea of scatter cushions, and of placing pillows and cushions to fill the gap between the two flat and surfaces of bedhead and bedcover we have the same concave making nest principle in mind.
Shapes emulating like the new moon, such as the crescent are to all intents and purposes concave.
In making soft furnishings and fashion garments the concave edges need to be clipped to take out the fullness so that they lie flat when the piece is turned to the right side.
Concave is the opposite of convex and in sewing the two work together. For instance, the stitched seam defining the outer curve of a round cushion during the making process when it’s worked from the wrong side is convex but when the seam is turned inside it becomes concave…