Beaglebone Green (Short as BBG) is a joint effort by Beaglebone.org and Seeed Studio and it was derived from Beaglebone Black (Short as BBB). If you've ever heard of BBB, you may know that BBB was the most popular board in the Beaglebone board family. It's much cheaper than previous version while inheriting all the great features of Beaglebone. BBG is better than BBB, for we kept almost all the good features of BBB such as the tiny size, abundant interface and strong expansibility, while at the same changed it a bit to make it more powerful.
The main change is replacing the HDMI interface with 2 Grove connectors. Grove is a great invention by Seeed because it's a modular standardized connector prototyping system by which you can build applications without soldering and jump wires.
Despite of the changes, BBG is still fully compatible with BBB and with all the BBB capes. Even though BBG has all these advantages, the price of BBG is much cheaper. What SeeedStudio wants is to provide a Beaglebone that is not only more powerful and easy-to-use but also reachable to most people. Please don't hesitate to choose BBG if you need a Beaglebone for your project.