One of the salient features of Mesopotamian art was their so called "artisitic iconography" and this meant that they made statues of gods or people in different sizes that reflected their importance and value. The larger the statue, the more important the figure. So in a group of smaller statues that were worshipped in homes or in temples, the important gods would be largest and the worshippers would in fact be relatively small.
These objects were not thought of the same way that we we think of art but they were viewed as functional in that worshipping them would provide benefits for the worshipper.
One particular feature of many Mesopotamian statues was the very large eyes that were important in helping the people consider them as live or sentient stand-ins for either gods or people that had died.
Mesopotamian art may look very crude and maybe even childish at times, but it is saying a whole lot through symbolism.
To describe some key features of the art itself, you can bet it is Mesopotamian if the robes are designed with simple vertical lines followed by spaced horizontal bars. The images are two dimensional, and much like Egyptian art are drawn with the people either directly facing you or turned to the side. People were drawn with bulbous eyes and men had very straight but curled beards. A lot can be sexually suggesting, and even sexually straight-forward. Their art was recovered mostly from cylindar seals, and stone reliefs.
Symbolism is seen throughout their art. A figure holding a certain staff may symbolize power (a shepherds staff often resembles kingship). The depiction of animals usually has a zodiacal significance, usually showing allegiance, opposition, or relation to a certain God of the zodiac. Wings often signified divinity.
Very simple acts can designate something very important in Mesopotamian art. Their artwork usually centered around people and a certain historical event or encounter which the population all would have known much about. They likely drew other, more personal and expressional art, but the art that survived was their historically crucial art.