To build up is to combine materials forming something larger. The words population, community, ecosystem and biosphere are in order from smallest component to largest and the combination of the first three builds a biosphere. A population is all the organisms of the same species, living in the same place. A community is all of the populations in a given area. For example, in a forest community, one could consider all the deer, pine trees, maple trees, squirrels and toads interacting together. The ecosystem takes into account the living or biotic community as well as the abiotic or nonliving factors such as air, water, soil, light, temperature, climate, etc. Ecosystems can be found in the water--aquatic ecosystems, or on land--terrestrial ecosystems. Some examples of an ecosystem are a temperate deciduous forest, a grassland and a desert. All the populations in the communities found in each ecosystem are adapted to the specific conditions of water, light, available food, soil, etc. Finally, the biosphere refers to the sum of all the ecosystems on Earth. Geologist Eduard Suess, in 1875 defined it as, "The place on Earth's surface where life dwells." Therefore, the relationship of the four terms is that populations make communities, communities are part of the ecosystem, and all the ecosystems build up to form the biosphere.
Well, generally speaking, when you build up anything, you are increasing the amount or productivity of some activity or quantity of something. In the terms you have provided, a population refers to a specific species of organisms, be it plant or animal. A "build up" in a population would mean the environmental factors that favor that organisms' survival and reproduction are very good, causing an increase in number. Two or more populations constitute a community of organisms, so an increase in populations would cause a build up in communities. The living and nonliving factors contained in an area would constitute an ecosystem. Nonliving factors would be the soil type, the water availability, the air being breathed. The largest division you have there is a biosphere, which could support several ecosystems within it. An increase from the grass roots level across the board would cause a build up within the biosphere itself, increasing the biodiversity.