Two dimensional artwork is the kind of art you typically see in a frame. I.e. it is flat or on one plane. Examples include watercolors, photographs, lithographs, oil paintings, etc. This artwork has a length and a width, but no depth or height.
Three dimensional artwork has depth or height in addition to length and width. Examples include sculpture, carvings, ba relief etc.
Some people make three dimensional art in a frame (e.g. some collages and some masks). These are still considered three dimensional.
The differences between 2-dimensional and 3-dimensional artwork are the differences between a painting and a sculpture. A painting, a drawing, a photograph, are all 2-dimensional, existing on a flat canvas or piece of paper, or on a wall, etc. A sculpture, a mobile, etc., are 3-dimensional objects that may be hung from or stand on a surface, but have length, width and height.
Paintings before the Renaissance: people saw in only a 2 dimensional figure, but in the Renaissance, people saw art in a 3 dimensional figure. Painters in the Renaissance gave attention to body size, proportions, perspective, and detail.
An octagon is 2-dimensional, an octahedron is 3-dimensional.
A square is a 2-dimensional figure, a cuboid is 3-dimensional.
Area is a 2-dimensional measure. Perimeter is 1-dimensional and volume is 3-dimensional.
A fractal in a 2-dimensional plane has a dimension between 1 and 2.
3-dimensional is not flat, like a cardboard box, while 2-dimensional shape is flat, like a face of a 3-D shape.e.g, a face of a box.
Rectangular prism is 3rd dimensional, while a rec. is 2 dimensional.
In 2-dimensional space, it is the difference between their y-coordinates, in 3-dimensional space, it is the difference between their z-coordinates.
Two dimensional is flat like a square and circle. Three dimensional is real life like, like a sphere and cube.
volume is a measurement of capacity, 3 dimensional. depth is a measurement of length, 2 dimensional.
A module is a 3-dimensional motif, and a pattern is a 2 dimensional decorative visual repetition.