The term "full stack" comes from the fullstack developer: a highly sought-after programmer who is fluent in multiple coding languages like Rails, Python, and Javascript. This very skilled developer is in high demand because he (or she!) can build applications, websites, etc. from start to finish. Different parts of the "stack" might need to be built in different languages, and the fullstack developer can code them all.
Marketers have stacks of their own, tied to each stage of pushing customers through their own company's marketing funnel. So to be a fullstack marketer, you have to learn the skills required to produce successful campaigns at every stage of your own company's marketing funnel.