Materials are used to define the way an object looks when rendered, and how the render engine will calculate the way light interacts with an object.

Blender Internal (BI)

The Blender Internal render engine has four main different ways to render an object, as a Surface, Wire, Volume, or Halo.
The default setting is Surface, which has many properties such as:

• Specular reflection

• Light Emission

• Z Transparency and Raytraced refraction

• Raytraced reflection

• Subsurface Scattering (SSS)

• Strand rendering

There are two ways to create materials for BI, with the Materials Panel in the Properties Editor, or with the Material Nodes system.

Cycles

Cycles uses a system of Shaders to create materials, with the ability to Mix and Add these and interact with other nodes.
A list of the Cycles Shader Nodes:

• Mix

• Add

• Diffuse BSDF (Bidirectional Scattering Distribution Function)

• Glossy BSDF

• Transparent BSDF

• Refraction BSDF

• Glass BSDF

• Translucent BSDF

• Anisotropic BSDF

• Velvet BSDF

• Toon BSDF

• Principled BSDF

• Subsurface Scattering BSSRDF

• Emission

• Background

• Ambient Occlusion

• Holdout

• Principled Volume

• Principled Hair

Cycles uses a more node based material system than BI, for example unlike BI materials, while you can edit Cycles materials in the Properties Editor > Materials Panel, doing so will actually create the proper nodes for your material (Where in BI material nodes are disabled by default)