The word qualitative comes from the Latin "qualis ?" meaning "what (is it) like ?"  When we answer questions like this, we often reply with statements like "it is circular", or "she is angry".  These tell something qualitative about the world.  Modern science has typically tried to eliminate qualitative statements in favour of precise quantitative ones.

However, according to René Thom, there are ontological and epistemological reasons for regarding the qualitative as not only independent of, but prior to the quantitative. See my own notes on this.

Note also the discussion of qualia in the philosophy of mind.