Biomes are nature's major ecological communities, classified according to the predominant vegetation, climate, and characterized by adaptations of organisms to that particular environment. Biomes are often defined by abiotic (non-living) factors such as climate, topographic relief (the shape of the landscape), geology, soils, and vegetation. Biomes may contain multiple ecosystems.
Biomes are extremely important and have changed many times throughout Earth's history. Anthropogenic (human) activities have recently been affecting biomes, which is a concern especially as energy use and greenhouse gas emissions continue to increase. Since these regions depend on a stable climate, climate change results in altered conditions within a biome.
There have been various biome classification systems devised over the years. The two most commonly used systems are the Walter classification scheme and the Whittaker classification scheme. The Walter system is based on the annual cycles of precipitation and temperature, along with the resulting vegetation that grows due to these conditions. The Whittaker scheme is based primarily on vegetation and is modified based on climate conditions. The common ground between these two popular classification schemes are the five major biomes presented below.
The Koppen-Geiger climate classification is a more complex classification system that is increasingly being used for dealing with climate change issues. This classification systems is very detailed, with multiple subcategories. This allows for much more fine-tuned classification, making it easier to show how the climate is shifting in a place over time. 
There are 5 major types of biomes:
Water is abundant all over the Earth, making up nearly 75% of the total biosphere. Life began in water billions of years ago, when the first molecules important for life came together. There are numerous species of plants and animals in aquatic environments, ranging from the deep ocean to shallow ponds. Aquatic biomes can be split into two categories - marine (oceans, coral reefs) and freshwater (ponds, rivers).
Deserts are extremely dry; they get less than 50 cm of rain per year. They cover about a fifth of the Earth's surface, and are typically found in mid-latitudes (around 30°N or S) due to the Earth's prevailing winds. Only specialized plants and animals are capable of living in these regions due to the lack of water they receive. It is rare for large animals to thrive here due to intense temperatures and lack of shade from the Sun.
Tundras are the coldest of the biomes. They ususally occur at high latitudes (above 60°N or S). They are characterized by low temperatures, frost molded landscapes, little precipitation, lack of nutrients, and short growing seasons. These characteristics lead to a general lack of biodiversity since only extremely well-adapted species of animals and plants can live here.
Forests are one of the more diverse biomes, with plenty of history and folklore centered around them. Forests cover a third of the Earth's land and contain over 70% of the carbon present in living things. The resources present in forests are valuable to humans, whether it be the wood itself for use as a fuel and other industry purposes, or the desire for the land occupied by the forest. This has lead to mass deforestation and pollution in once-thriving ecosystems.
Grasslands are lands dominated by grass rather than trees or shrubs. There are two main types, the savanna (tropical) and temperate grasslands.
Savannas cover almost half the surface of Africa and portions of Australia, South America, and India. They are characterized by hot climates with consistent rainfall for 6-8 months, followed by months filled with drought.
Temperate grasslands have almost no trees, and have less rainfall than savannas. Temperatures vary more from summer to winter as well, with very hot summers and very cold winters. Temperate grasslands can be found in the prairies of North America, the pampas of South America, and the steppes of the former Soviet Union.
UC Berkeley has biome pages with additional information on these topics: