Social factors
The economics of music changed, too. Composers wrote for patrons and used local musicians known to the families concerned. Parts had to become simpler - with occasional pieces for virtuosi on particular instruments.
Notation
Melody lines were notated in increasing detail with phrasing and dynamics.
Movements were unified with distinctive moods and rhythms or tempo.
The Baroque habit of making each movement devoted to a single "affect" or emotion faded away. Form as we know it was born - contrasts between sections, key changes, stridently rhythmic themes next to lyrical ones...
Try to play a movement from a sonata by one of these great classical composers for the piano:
Clementi