In the early Celtic art the images were flattened, very much like the Byzantine art in how they were aiming for communicating ideas rather than portraying realism. The scrolling flowers and trees reminded me of the classical roman relief carvings that represented abundance and fertility.
Carolingian art started to bring back the classical style of creating depth, and started showing people in more natural poses instead of just showing them head-on. A great example is the image of St. Mark in the Godescalc Gospel Lectionary.
Charlemagne encouraged artists to study and copy the classical artists when illuminating their manuscripts. They ended up playing with light and shadow, and created more dynamic images than in the earlier Middle Ages.