A convex shape is a geometric figure that curves outward, with all points on the shape's surface or boundary pointing away from an internal point. In a convex shape, any line segment connecting two points within the shape lies entirely inside the figure. Convex shapes include common objects such as circles, ellipses, and regular polygons like squares and triangles. Convexity is an important concept in various fields, including mathematics, physics, and computer graphics, as it often simplifies calculations and analyses.