Material design is a Design language developed by Google to bridge the communication gap between user and device. It contains Light and Shadow, Color, Quantum Paper, Transformation which is similar to the real world.This will help the user to sync with real world stuff.I will explain all these points :-
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Light and shadow of an object is projected in every 3D space in the real world.(explain it more).
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Color of material is paint on canvas. A quantum paper is amount of paper involved in an interaction with user.
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Transformation is how material can be transformed to one place to another.
For mobile device with Android Platform this link will give you detail explanation to implement into app. Simillary, For ios platform .
For web components, I would recommend Polymer, as it gives you flexiblity to create your own element or use element created by others to add in it. Element is a bundle of CSS, HTML and Javascript; these are the bulding block of an web page which can be reused. With the help of element, a developer can reduce his time to build the web page. you can use one or more element to combine and make something good out of it. similary, ‘materlize.css’ will reduce the complexity to give style layout and color.
You can integrate it with many other Frameworks. There is integration and support for other frameworks like Angular, Node,Laravel in this platform. This link will give you the idea about: Material with angular and Material UI
Material Design Lite is where you will get the same material feel as real life with decreased loding time for the result to display any device which resulting in good user experience. Click here to know more.
I would like to conclude by saying that it is easy to implement and use which helps both user and developer in design for logical world.