If you still are seeking a clear answer to your question, I think I can answer it more clearly than a lot of website sources.
Modernism began at the end of the 19th Century and was influenced by the new technologies and ideologies that permeated the period (automobile, airplane, telephone, radio, telegraph, theory of relativity, theory of evolution, Marxism, and Freud's views about the unconscious). The result of these influences was that artists felt they no longer had to adhere to strict conventions of what needed to go into creating a painting, sculpture, architecture, music, and so on. In other words, "tradition" was no longer a sacred cow. While traditional art and all tradition, for that matter, emphasized the importance of continuity -- that is, one generation should more or less maintain the same standards and practices of the previous ones, modernism suggested art must be investigative, similar to the way new technologies and ideas were investigations, so that the arts and what artists did could now be greatly expanded -- basically to art became 'whatever you could get away with.'
Postmodernism was a response to decades of modernist art. What postmodernism asserted (during the second half of the 20th Century) was that there were no new ideas or forms to be found in art, as 100 years of experimentation were enough to explore new forms, so that creating something "new" or "modern" would simply be a benign and insignificant variation of something that was already investigated or created. Thus, postmodernist critics claimed newness was "exhausted." They did claim, however, that the next logical progression in the arts and for the activity of artists was to borrow, combine, refer to, imitate, comment on, etc., previous works of art. So, postmodern artists should no longer seek entirely new means of creating art, but artwork would now become an investigation of what was already new. A secondary idea of postmodernism is/was that the creator or artist should no longer be considered as being "creative." Rather, creativity was a natural aspect of being, so that an artist, if she/he tuned into this vast pulse of creativity, would be more of a vehicle for transmitting principles of art.
That's the short version, anyway.
; < )