Academic art is not a movement per say, but it it is a term that has come with the advent of European and notable French style elitist academies. In various contexts academic art is used as a derogatory or pejorative term as much as its opposite.
To some it simply means the act of conforming to a schooled, educated, and formal approach to art such as that obtainable at an art acedemy.
Academic art is also known as style of sculpture and painting produced under the influence of the French Académie des Beaux-Arts. The artists practiced under Neoclassicism and Romanticism.
Please note that ‘academic art has since then ended up meaning different things to different people. To some it now means andy art:
1 influenced by academies in general
2. all new styles which are being embraced and adopted by academies.
You can read more about art movements here