Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.
Any object or surroundings or space can be
Onedimensional (or 1D)
Twodimensional ( or 2D)
Threedimensional (or 3D)
For example,
A point is a zerodimensional object as it has no length, width or height. It has no size. It tells about the location only.
A line segment drawn on a surface is a onedimensional object, as it has only length and no width.
The 2dimensional shapes or objects in geometry are flat plane figures that have two dimensions – length and width. Twodimensional or 2D shapes do not have any thickness and can be measured in only two faces.
A square, circle, rectangle, and triangle are examples of twodimensional objects. We can classify figures on the basis of the dimensions they have.
In geometry, threedimensional shapes are solid figures or objects or shapes that have three dimensions – length, width, and height. Unlike twodimensional shapes, threedimensional shapes have thickness or depth.
A cube and cuboid are examples of threedimensional objects, as they have length, width, and height.
Take for example a cuboid,
The attributes of the cuboid are faces, edges, and vertices. The three dimensions compose the edges of a 3D geometric shape.
Some examples of threedimensional shapes:
3D shapes  Examples  
Cube 
Rubric cube 
Dice 
Sphere 
Ball 
Round 
Cone 
Carrot 
cone

Rectangular prism and cuboid

Book 
Gift 
Every threedimensional figure houses many twodimensional figures. We can by joining together many twodimensional figures we get a threedimensional figure.
Fun fact

Let’s do
Identify twodimensional shapes within the threedimensional shapes given below.