From my modest knowledge: A study of populations. Btrithrates, deaths, migrations etcetera. Often demographers make prognoses of future population develoments, not least growth or decline in total numbers. But perhaps demography is more of a "historical" science than anything else? If only statistics of sufficient quality is available demographers can get an excellent record, and contribute greatly to our understandment of past and present society, but should deal more cautiously with the future, because human behaviour changes very fast (and perhaps more unpredictable than scientists like it). How healthy lives they live, when - if - they get a partner and kids, where they move for what reasons, etcetera. Even between countries we expect to be "similar" (perhaps European)there is big differences in prognosis for population development, some had a minimum birthrate some years or decades ago, others perhaps now.
But perhaps demography is more of a "historical" science than anything else? Demographics or demographic data refers to when an goal selected population characteristics as used in government, marketing or opinion research, or the demographic profiles used in such research. Note the distinction from the term "demography" (see below.) Commonly-used demographics include race, age, income, disabilities, mobility (in terms of travel time to work or number of vehicles available), educational attainment, home ownership, employment status, and even location. Distributions of values within a demographic variable, and across households, are both of interest, as well as trends over time. Demographics are frequently used in economic and marketing research. Demographic trends describes the changes in demographics in a population over time. For example, the average age of a population may increase over time. It may decrease as well as certain restrictions may be in place, for instance in China if the population is high. The term demographics as a noun is often used erroneously in place of demography, the study of human population, its structure and change. Although there is no absolute delineation, demography focuses on population structure, processes and dynamics, whereas demographics is most often used in the fields of media studies, advertising, marketing, and polling, and should not be used interchangeably with the term "demography" or (more broadly) "population studies". http://en.wikipedia.org/wiki/Demographics