Created by Nvidia, MDL stands for Material Definition Language. It is a language is meant to describe the property of a physically based material, and how it is supposed to behave. The goal of MDL is to provide a portable method of defining materials, ensuring they look the same across different rendering engines and applications. MDL is not a shading language like HLSL or GLSL, as it does not define the behavior of the light itself. Light and material are generally extremely dependent to each other, which can affect the portability to another platform. More information about Material Definition language can be found on the Nvidia website.
MDL Graphs were introduced in Substance Designer 5.5, making it the first and only nodal MDL authoring application. Substance Designer allows rendering and material artists to explore new possiblities, improve their iRay renders and turns Substance Desginer into a material hub application for different rendering targets.
Below some examples of MDL applications can be seen.
This metallic clearcoat material is impossible to define only through textures. It features two separate specular highlights that behave completely different: one rougher metallic coat with speckles, and one very smooth clear topcoat. Before MDL this would have to be explicitely set up in your target rendering application, but now it can be defined and exported from Substance Designer. There is a tutorial on Academy on creating this effect yourself.
In this example showing a Malachite with Chrysocola rock, MDL was used to define the very specific colored, anisotropic highlights on the cut tops of the rock. This example is completely explained on Substance Academy.