A 3-dimensional object in mathematics is a shape that has three dimensions: length, width, and height. Some examples of 3D objects include cubes, spheres, pyramids, cones, cylinders, and prisms. These objects can be described using mathematical formulas and equations, and their properties such as volume, surface area, and angles can be calculated using mathematical methods. 3D objects are commonly used in geometry, physics, engineering, and computer graphics.