In a nutshell, it means that spiritual and intellectual formation is more important than the material that you learn and remember.
Here's what Laura Berquist had to say about it in Designing Your Own Classical Curriculum (referring to Dorothy Sayer's article "The Lost Tools of Learning" click here to read Sayers' article)...
The most impressive of the many things Miss Sayers said was that the goal of education should be to teach children how to think; we want them to learn the art of learning. Then they will be equipped for life; whether or not they learn all the subjects possible in school, they will be able to learn any subject when it becomes necessary or desirable, if they know how to learn...In fact, she goes on to say, learning subjects in school is of very secondary importance. (pg. 13)
You can read the rest of the Introduction to Laura Berquist's Designing Your Own Classical Curriculum here.
Fran Crotty of Kolbe Academy has a beautiful quote that ties in the spiritual side of education as formation (from Implementation of Ignatian Education in the Home)...
It should be the objective and is definitely the responsibility of every rational Catholic mother and father to see that the child is educated, so that he can be truly Catholic with the consent of all his faculties.
It's not hard to see that this makes sense on a practical level, even if our 20th-century-conventional-school-trained brains want to fight against it on some level. If our children learn to love learning, develop habits helpful to learning and practice virtues like patience and perseverance; if their education helps them develop problem-solving skills, critical thinking skills and the confidence to overcome "road-blocks" that they encounter...these things will help them succeed in life in practical and spiritual matters. This philosophy looks at the child as one whole being with intellect, will, memory, imagination and conscience all working together.
It has rather delightful consequences too, for stressed-out homeschooling moms. What stresses us out most? It's "filling in the gaps" - making sure they have (figuratively speaking) all their i's dotted and their t's crossed. The good news is that, if they're working on developing these habits (sometimes of their own initiative, sometimes because they "have" to - ideally a little each day), if they are learning things and progressing and practicing virtues and all that (even if it be in their own seemingly snail's paced way) - then you are helping them do what they should be doing, even if you don't finish every book or meet everyone else's expectations for your child.
I don't know why it is predominantly "classical educators" that talk about this concept (although it is certainly hinted at in other methods such as Charlotte Mason, Montessori and unschooling). For me, the idea of formation as the primary goal of education is common sense, it is Catholic, it is true.
Please feel free to comment with additional ideas and clarifications. It seems that I should include more caveats and explanations, but I'm not sure that these wouldn't confuse the matter further.