The meaning behind most of the art in both Mesopotamia and Egypt in the 3rd millenium was religious symbolism and representation of the peaceful aspects of daily life. There are many statues of royalty and gods found in both cultures. Egyptian art has more statues of common people than Mesopotamia. The use of both cultures writing systems is found in their artwork.
Many aspects of Mesopotamian art had practical uses, one of which is the cylindrical seal. These seals, as the name says, are cylindrical and they have raised images that vary greatly between seals Some of these seals were quite small and worn as protective amulets or jewelry others were large and used for decoration. Many show gods, animals, mythological stories, and daily life. These seals were made to be rolled onto a surface that was usually wet clay, generally for identification or decorative purposes. They were used quite like you use your signature is used today. (http://lib.hope.edu/record=b1117476~S4)
One of the most famous works found from this era and from ancient Mesopotamia in general is called the Standard of Ur (top and bottom picture to the right). It is a two sided mosaic with each side depicting two very different scenes. The first side (top right picture) depicts war. In the center of the top panel there is a figure that is larger than the rest. He is probably a ruler, or leader. This occurs in Mesopotamian art frequently, showing important people and rulers larger than the rest and near the top of the piece. This is an example of hierarchical perspective in which the more important people are shown larger generally near the top of the piece and less important people, and sometimes animals, are smaller. The rulers chariot is behind him and naked prisoners are being presented to him by his soldiers. The prisoners being naked is a symbolic way of showing their degradation. The second panel is of prisoners killing off the enemy and taking people as prisoner. The lowest panel shows men in chariots running over the enemy. The war side of the mosaic seems to be moving in a left to right direction showing the destruction soldiers and war can make. The second side of the Standard of Ur (bottom right picture) depicts animals and people that seem very peaceful and serene. Agian, the top section has one figure that is larger than the rest, as he is more important. This panel seems to be depicting a banquet. The second and third panels show Sumerians with animals and fish. The animals are representative of good land and fertility. The two sides of the Standard of Ur are very different but they represent a king or ruler and how he must be able to protect his people and land in times of war and how he is responsible for fertility and peace.(http://lib.hope.edu/record=b1296675~S4)
Egyptian art is generally found to show how sophisticated their society was. Because of this many scenes depict social harmony. Many pieces show family affection and religious symbols are used in art work a lot. Most scenes depicted are peaceful and are not violent. The most violent scenes in egyptian art generally show nothing that is worse than butchering an animal or the overthrow of an evil. Egyptian art uses a lot of symbols, many of which are hieroglyphics, their writing system.
Many larger Egyptian pieces are carved into flat limestone surfaces and are sometimes painted. The picture to the top left, a carved relief of Nebhepetre Mentuhotep is an example of this and use of hieroglyphics in artwork. His curved beard shows that he had joined the gods when this relief was created. (http://lib.hope.edu/record=b1416223~S4)
An interesting aspect of Egyptian art is how they paint people with different skin tones depending on where they are from. Asiatics are painted light yellow, African peoples are generally painted black, Aegean and Egyptian people are painted a reddish brown. Egyptian women are usually painted a pale ocher and overlapping peoples are usually given varying skin tones as to differentiate one person from another. This amount of differentiation in skin color is very interesting for the time. Egypt is one of the few cultures to do this, especially to this degree. Another interesting part of Egyptian art is its statue work. Most statues represent royalty, kings, and gods. The Great Sphinx, (bottom left picture) while not a statue of a human, is representative of great kings. ( http://lib.hope.edu/record=b1416223~S4)