What is a logistic function?
A logistic function is a form of sigmoid function typically found in modelling population growth (see below).
Here is the graph of a typical logistic function:
The graph starts at some base population and grows almost exponentially until it begins to approach the population limit imposed by its environment.
Note that logistic models are also used in a variety of other areas (e.g. neural network analysis, etc.) but the growth model application is probably the easiest to visualize.