Shape communicates on flat surfaces and in three dimensional spaces. Shapes do not exist by themselves; they have color, texture, transparency, scale, and perhaps patterns and motion. Beyond the basic shapes described here is a lot of room for complexity and interaction. This is to get you started thinking about shape.
Circles and curves: A circle has no beginning or end, and is the shape of eternity. It represents a whole, and can be separated into parts. Curved shapes are natural and organic, and can communicate growth.
Squares and right angles: Use right angles to represent solidity and stability. A city skyline is primarily made up of right angles. Square shapes are associated with cold, hard surfaces.
Triangles: To represent movement, progress, or aggression, use triangles. Their connotation is derived from arrowheads and mountain peaks. Triangles are active shapes.
The 2D shapes described above have 3D counterparts that have similar meanings. In addition, three-dimensional shapes have weight or mass.
These concepts are familiar to visual artists, and can translate into other forms as well. Music, light, storytelling can all have shapes.