To specify the terms above, let's take a look at the word formation below and please compare.
The word "edification" is derived from the word "edify" that means as the following:
edify
v. educate morally or spiritually, provide moral guidance, strengthen, improve
http://search.babylon.com/?q=edify&s=dict&babsrc=home
v. [T] fml or humor to improve (the mind or character of)-Longman-Dictionary of Contemporary English p.325

Literally the meaning of the word "edification" is:
n. moral guidance, moral improvement, strengthening and building up of character. It's based on http://search.babylon.com/?q=edification&s=dict&babsrc=home and n [U] fml or humor the improvement of the mind or character. It's based on Longman-Dictionary of Contemporary English p.325

While the word "education" is derived from the word "educate" that means as the following:
v. to teach or train esp. through formal instruction at school or college; provide with education or instruction (Longman-Dictionary of Contemporary English p.325) and
v. instruct, teach, train (http://search.babylon.com/?q=educate&s=dict&babsrc=home)

Literally the meaning of the word "education" is:
1. the activities of educating or instructing or teaching; activities that impart knowledge or skill; "he received no formal education"; "our instruction was carefully programmed"; "good teaching is seldom rewarded"
(synonym) instruction, teaching, pedagogy, educational activity
(hypernym) activity
(hyponym) coeducation
(part-meronym) classroom project
(derivation) educate
2. knowledge acquired by learning and instruction; "it was clear that he had a very broad education"
(hypernym) content, cognitive content, mental object
(hyponym) physical education
(derivation) train, develop, prepare, educate
3. the gradual process of acquiring knowledge; "education is a preparation for life"; "a girl's education was less important than a boy's"
(hypernym) learning, acquisition
(hyponym) acculturation, assimilation
(derivation) train, develop, prepare, educate
(classification) instruction, teaching, pedagogy, educational activity
4. the profession of teaching (especially at a school or college or university)
(hypernym) profession
(hyponym) teaching, instruction, pedagogy
(derivation) educate
(classification) instruction, teaching, pedagogy, educational activity
5. the result of good upbringing (especially knowledge of correct social behavior); "a woman of breeding and refinement"
(synonym) training, breeding
(hypernym) upbringing
(derivation) educate, school, train, cultivate, civilize, civilise
(http://www.babylon.com/definition/education/English)

The differences are clear enough if we compare the above definitions. "Edification" mostly concerns with the moral or character building or improvement formally and informally while education concerns with the gradual process of acquiring the knowledge.

In bahasa Indonesia I dare to say that the word "edification" means "bimbingan moral atau karakter" or "perbaikan moral/ karakter" while the word "education" means "pendidkan" that generally happens at formal school.