As implied by the term 'classical', the music of this period looked to the art and philosophy of Ancient Greece and Rome - to the ideals of balance, proportion and disciplined expression. The late Baroque style was polyphonically complex and ornamental and rich in tis melodies. Composers of the Classical era deviated from the evolution of their predecessors - their music had a considerably simpler texture. It's a bit of an irony that two of J.S. Bach's children, Carl Philipp Emanuel (C.P.E.) a Johann Christian (J.C.), belonged among the leaders of the new Classical movement. Their father was the greatest figure in the Baroque style and thanks to the new era of his children, he became old-fashioned.
Homophony - music where the melody and accompaniment are clearly distinct - was the main style during the classical era; new genres were discovered that completed the transformation from the Baroque era to the Classical. The sonata was the most important of these, as well as the most developed. Although Baroque composers also wrote sonatas, the Classical style of sonata is completely distinct.

The foundation of the Classical sonatas is conflict - for instance between two themes of contrasting character. The contrast during the performance of the sonata increases, until it is finally "resolved." The sonata allowed composers to give solely instrumental pieces a dramatic character. All of the main instrumental forms of the Classical era, the quartet, symphony,and concerto, were based on the dramatic structure of the sonata.
One of the most important "evolutionary steps" made in the Classical period was the development of public concerts. Although the aristocracy would still play a significant sponsoring role in musical life, it was now possible for composers to survive without being the permanent employee of some noble or his family. It also meant that concerts weren't limited to the salons and celebrations of aristocratic palaces. The increasing popularity of public concerts led to a growth in the popularity of the orchestra as well, to the enlargement in the number of musicians and the number of orchestras overall. Although chamber music was still performed, the expansion of orchestral concerts necessitated large public spaces. As a result of all these processes, symphonic music (including opera and oratoria) became more extroverted in character.