D3 stands for Data Driven Documents. You should use D3.js when your webpage is interacting with data. You can explore D3.js for it’s graphing capabilities by checking the official D3.js site at d3js.org.
Mike Bostock wrote D3.js based on his work during his PhD studies at the Stanford Visualization Group. Mike now works at The New York Times who sponsors his open source work. That is why The New York Times has published many cool intuitive data analysis examples with D3 visualization . You can find Mike at the github site. While he wrote the library, there are many contributors that are adding a diverse set of components and plugins.
You can do a google search to find out what the d3.js can do to present and analysis your data.
A beginner tutorial: http://www.dashingd3js.com/
More D3.JS gallery: https://github.com/mbostock/d3/wiki/Gallery