Abiotic means not living, so when a scientist is talking about abiotic verses biotic factors within a particular ecosystem (biome) they are referring to the the living and non-living factors that affect that area.
Abiotic factors could be all kinds of things. For example: wind, temperature, rainfall, ground water, humidity, amount of sunlight, soil composition, intensity of daylight, air pollution, noise pollution, etc.
A terrestrial biome is a land biome (vs an ocean/lake/stream) biome. Any of the above will affect the biome, but a large contributing factor is the amount of rainfall. When you look at a world map, the Sahara desert and the South American rain forests are at about the same latitude, but the biome that is present is extremely different. The abiotic factors of temperature and amount of sunlight are more or less the same, but it is the amount of rainfall received that allows the rain forest to be a tropical paradise and the Sahara to be quite barren.
The location differences of biomes don't have to be separated by great distances either. Sometimes two very different biomes can be separated by mere feet. For instance at high mountain elevations, pine forests are quite common, but above a certain elevation, those trees can't survive. That elevation creates a "tree line." Below that line, the abiotic factors allow for the presence of a lush and diverse biome, but above that tree line the temperature, rainfall, wind, etc. allow for little more than lichens to exist.
An abiotic factor is a factor in the environment that is not living. This include things like air, water, rocks, sun, etc.; anything that is not biotic, or alive in anyway. Even if these things are not alive they still contribute to the biome they are in. The biotic factors could not survive without the abiotic factors: they need air to breathe, water to drink, sun to make food (for plants), sun to help herbivores survive, rocks/shells to provide shelter, etc. Depending on the biome, different abiotic factors are needed more than the rest (like rain forests vs. deserts), but every abiotic factor has a purpose.