And can it be implemented in the public schools? The answer to the second question is yes, according to Alaska's Chugach School District. As you can see in the Edutopia article, rather than grades, Chugach students have "tote around report cards as thick as history texts. Each packet details the individual student's progress through the district's more than 1,000 learning standards as they move from kindergarten to high school graduation." Once students have mastered all the concepts in the standards, they graduate, whether they're 16 or 22.
Answering the first question second, standards-based education is when individual student's achievement is measured against a standard (duh), usually set by the state or local board of education. The most familiar instance for most people would be high school graduation requirements--4 years of English, three years of math, etc. etc. But even those "standards," measured in years, are rewards for seat time rather than learning.
This is an issue for all kids, not just the gifted. Anyone can do the bare minimum amount of homework, score averagely on tests and mostly sit in the back of the classroom doodling or passing notes and accumulate three years of seat time in math classes (BTDT). Allowing children to do that (or, in the case of gifted children, expecting them to do that) is a great disservice.
Some of the greatest thinkers of our time, like Tom Magliozzi from Car Talk, are starting to realize that the way we teach needs to change. Read his New Theory of Education rant. He actually goes a step further than external standards/benchmarks and suggests that learning should be tailored to every learner, as the best way to make people want to learn is for them to be interested in the subject they're learning in the first place. Though he's still speaking in terms of school, his ideas are edging perilously (some might say) close to the unschooling philosophy, where all learning is interest-based.
It would be difficult to turn all public schools into tailored-learning centers. However, there are current standards that teachers have to address in their lessons. I think if the school boards were more upfront about what the standards are, the kids would be able to decide how to meet them while pursuing their own interests, guided by the teacher, rather than being led by the nose or, worse, ignoring him/her altogether.