A fungus is a multicellular organism that has cell walls similar to plants but does not have the ability to make its own food via photosynthesis. As a result, and because they are not mobile, fungi survive by growing directly over their food source; in a lichen, algae serve this role. "Algae" is a broad term for any single-celled organism that can photosynthesize. This includes both simple, prokaryotic organisms (like bacteria) and more complex --- but still single-celled --- organisms called protists.
Lichens are classified based on their body type; specifically, it is the thallus (the fungus structure) that defines the lichen. Fruticose lichens are lichens that grow in three dimensions and do not have a clear division between their upper and lower surfaces. Foliose lichens are flat on the surface, but have a clear division because they grow in layers. Crustose lichens grow in a crust over the surface.
Lichens grown on hard, solid surface likes rocks, bark and even man-made structures like sidewalks. Lichens have been found in every environment on Earth, including in the extreme temperatures of deserts and the Arctic. Different types of lichens need different types of environments, however, the main reason they can survive in inhospitable climates is because the lichen does not need much more in the way of nutrients than what is provided by the two organisms in the symbiotic relationship.
Lichens are extremely important in several types of ecosystems. Because they do not need much more than the component organisms to survive, they are often the most basic organism found in harsh terrains, and thus are food sources for animals in the tundra and desert. Additionally, lichens help with the nitrogen cycle, which in turn ensures fertile soil for plants in which plants can grow. Dead lichen are also recycled as organic material in the soil, which furthers helps increase the viability of the soil.