Population is the members of a given species of animal in a defined geographical area. This can be at the local level and at the regional level. Populations tend to have fuzzy boundaries, with the traits marking a particular population being more marked in the middle of the population and more transitional along the boundaries. Biologically, humans are best thought of in terms of populations rather than as races, as races are sociological rather than biological constructs.
The initial colonization of an area by a spcies is known as a pioneer population, depending on the degree of isolation of that population, this can lead to significant genetic drift, as well as adaptation to new ecological challenges. As populations spread you frequently can have interbreeding of populations along boundaries, but inability of more remote specimens to interbreed.
Populations are shaped by birth, deaths and migration (including immigration and emigration). They are shaped by natural events such as disease and natural disasters.
Populations will frequently achieve a balance or equilibrium for long periods leading to stability, but new competition, environmental change such as climate change, natural disasters, or increased predation can lead to dynamism that can knock the population out of equilibrium.
A population are members of a species that inhabit the same area at the same time and are capable of interbreeding. They are adapted to a set of conditions for their environment. You can have different populations of a single species of frog--one can be the warm adapted population living down South and one can be the cold adapted population living further North. Although they are technically the same species, over time and due to geologic separation, they may accumulate enough differences that they may no longer be capable of breeding together. This may eventually form a new species due to natural selection. Sometimes, when brought back together, the two populations can form a zone of hybrids. However, members of a population share many adaptations that help them to survive in the habitat they are born into.