The life level of a world defines (in very broad terms) how advanced native life is on the world. It ranges from no life at all, through simple single celled organisms, to land animals and extensive (Earth-life) conditions.
Organic and Archaean are quite common on worlds that could potentially support life, but life becomes significantly rarer as you move up through the classifications.
The evolutionary path on worlds can be very different in the details, but the initial steps are broadly similar at the high level. Diversity really comes in beyond the Aerobic stage.
For a list of types of life, see: Animals, vegetation
Organic Chemicals originally formed, which were simple amino acids. Most worlds with liquid water will form basic organic molecules like this, but few progress any further. Such worlds have an Organic classification.
Prokaryotes are the first living organisms, and include bacteria, as well as earlier forms. On many worlds, Prokaryotes is as far as it gets, and it can take billions of years to evolve anything more complicated. The presence of Prokaryotes are a marker for Archaean worlds.
Over time, colonies of singled celled organisms may form something similar to Algae or slimemolds. These may start producing oxygen as a by-product.
Protozoa are multi-celled organisms, and are generally the sign of Aerobic worlds since they generally don't form until there is sufficient oxygen in the environment.
EoGaian worlds are pre-Aerobic, with a mostly methane atmosphere. Once the life classification changes from Archaean to Aerobic, then terrestrial worlds are classed as MesoGaian.
With the rise of oxygen, so the Aerobic stage is reached. plankton consumes smaller life forms, forcing the evolution of larger and more complex organisms. Larger varieties of algae becomes seaweed and jellyfish evolve. Eventually, the arrival of simple marine organisms, such as starfish, sea urchins and worms marks the last stages of the Aerobic classification.
The Complex Ocean period is heralded by the arrival of crustaceans, fish and other free swimming vertebrates.
The above assumes that things progress in much the same way as they did on Earth. This is unlikely, but easy. The above categories probably fit most evolutionary paths, however the details of each are unlikely to be the same on all worlds - e.g. when grasses first evolve and so on.