I don’t know which living organisms you are dealing with. In any case, based on my specific interests, I like the generic definition of demography as the statistical study of population dynamics useful for understanding how populations respond to changes in the biotic and abiotic environment. The population dynamics describes how a given population size changes over time, controlled by birth, death, and migration. I work on fisheries and hence my examples regard such world.

I attached a file with some considerations that I hope will be useful for your needs

The large context of demography involves the entire environment, as mentioned in the answer above. Considering the restricted "movers" which demography analyzes, I believe it essential to understand which age-related variables may explain births, deaths and mogrations. From these age-probabilities of events you will get the most interesting aspects of your populations. If the data is sufficiently robust, try a life-cycle approach.

 My experience is limited to human demography.  The following parameters are enough to predict the behavior of population:

1)     age-sex distribution

2)     age-sex specific mortality rate

3)     age specific birth rate for women

Of course, we do not always get enough data to estimate the above parameters. For instance, instead of age-sex distribution, we may have to suffice us with the number of women before puberty, that of women in reproductive period, and that of women after menopause.

I hope this will be of some help.

My experience is also limited to human demography. Your question is quite complex and depend largely on the model you ar using and on the level (national level or regional). If you are working at national level and using a basic model, you need

1. Age-sex distribution

2. Age-sex mortality rate and is evolution until the end of your projection

3. Age female birth rate and is evolution until the end of your projection

4. An estimation of international immigration and emigration by age-sex for each year until the end of your projection.

If you are working at regional level, you need also an estimation of internal immigration and emigration. 

In my experience (based on studies on long lived species Octocorals an Cetaceans) the main population parameters neded to be known are: Population structure (in size/age classes or in life stages), population density, age at first maturity, fecundity and fertility,  mortality and population reproductive output.

In addition, Lloyd Demetrius introduced 2 more demographic parameters in 1974-the entropy and the reproductive potential of a population. The entropy of a population measures the variability of the contribution of the different age classes to the stationary age distribution. The reproductive potential measures the mean of the contribution of the different age classes to the growth rate.