Growth Hacking is the new term for marketing in a startup setting. In effect it acknowledges the extreme uncertainty of the startup environment, and describes the process in which startup marketers use digital and quantifiable marketing techniques such as search engine optimization, web site analytics, A/B testing and content marketing to drive sales and revenue growth.
Growth hacking is different from old-school marketing in that it is extremely technical and quantitative. A growth hacker is obsessed with revenue growth and the metrics that affect this growth.
Neil Patel has a great article that explains what it means.
The Next Web has a great article that goes into greater depth about growth hacking.