A population is all the individuals of one species in an area. A community is all the populations living together. We can rarely count every individual, so we estimate from samples, which must be random to avoid bias.
A population in a new habitat grows slowly, then exponentially, then levels off. The level it stays at is the carrying capacity, the largest population the environment can support. Growth is slowed by density-dependent factors such as competition, predation and disease, which get stronger as the population gets more crowded.
Members of a community affect each other through competition, predation, herbivory, parasitism, pathogenicity and mutualism.