the dynamics of population is how the number of individuals of a species within a population will evolve in time.
Dynamics of population is the science that consider mortality and natality rate of a population and how it vary due to every possible factors.
For instance with a given natality rate and mortality rate for a population in a full of ressources environnement, the basical ecological model of population dynamics should be an exponencial growth
If you consider that there is not enough resources in the habitats for an infinite number of individuals there will be a threshold called carrying capacity. if the poplation goes above the carryig capacity(overshoot),the lack of ressources ( food, place ect...) will cause mortality and get the number of indivinduals beneath the carrying capacity.
You can also get the model to be more realistic by considering stochasticity wich is the radom probability of event link to the envirronement to happend and impacting the dinamics of the population. This could be represent by a stadar error on your graphic ( see the several differents possibility on the next graphics that come from differents simulation with radom stochasticity)
there is a lot of different way to add complexity to a studies of population dynamics in order to make it closer to your subject of studies ( see lotka & voltera for predation and competition as a start :) )