The major significance of standards in the field of education is that they are very important to ensure that all students are actually learning what they are supposed to learn. Standards are also somewhat controversial in some respects.
For a long time, the US lacked any consistent standards in its educational system. States were allowed to create their own standards and those standards could be as high or low as they liked. In 2001, the Bush Administration passed the No Child Left Behind law that required states to meet certain standards. By doing so, the administration was trying to ensure that all students would learn the sorts of things that they really need to learn. This is important in education because without standards it is too easy for schools to pass students even if they do not know as much as they should.
These standards have become somewhat controversial for a number of reasons. Many feel that too much emphasis has been put on these standards and on the standardized tests that measure them.
Standards, then, are important to ensure that students are learning as they should, but they can be controversial because people can disagree on what the standards should be and how they should be enforced.