Aristotle divided all living things between plants (which generally do not move), and animals (which often are mobile to catch their food).

However today we are more scientific in our definition:

* The greatest difference between plant and animal cells occurs at the cell membrane. The cell membrane of a typical plant cell is covered with a protective wall of cellulose. The cellulose makes the membrane stiff, and thus the plant cell's structure is very rigid. This gives plants stiffness, and allows them to grow tall. Cellulose is secreted by the plant cell's cytoplasm. Thus, the plant cell has a cell wall, while the animal cell does not. The plant's cell wall may also contain lignin, a component of wood. The cell wall allows a very large pressure to be built up inside the cell, through osmosis. Animal cells, on the other hand, have more flexible membranes. So animal cells are much more diverse in their shapes.

* Most of the space inside plant cells is made of of a large vacuole containing cell sap. Vacuoles in some types of plant cells serve to build stalks and stems. Animal cells never contain large vacuoles.

* Plant cells contain plastids. Animal cells do not. The most noteworthy plastids are chloroplasts. These contain chlorophyll, a green chemical necessary for photosynthesis, which also gives plants their colour.

* Animal cells have centrioles, which help in mitosis. Plant cells do not.

* Plant cells have glyoxysomes. Animal cells do not.

At one point, organisms were simply through of being either plants or animals. In this day and age, we scientifically place organisms into more than those two categories (consider that there are fungi, protists, and bacteria, and none of these are technically plants nor animals) making it a bit harder to simply point out the absolute differences between plants and animals. Though, I think omnichronos is correct in pointing out that most of the major differences between plants and animals (and other organisms) lie at a cellular level. Perhaps another important factor that these lifeforms is that most plants can perform photosynthesis, whereas most other organisms depend on consumption of some form for their energy.

By the way, it's erroneous to say that plants don't "breathe" oxygen. Yes, plants most certainly take in carbon dioxide, but this is for photosynthesis--chemical energy production (or as elementary school teachers say, "food production")--not for respiration; oxygen gas happens to be one of the "waste" products of this process. Though, like animals, plants need to intake oxygen as part of their respiration.

Breathing..we breathe Oxygen..plants breathe CO2