Applied mathematics is a field of mathematics which uses mathematics to solve problems of other branches of science. The contrary notion is pure mathematics. There are many fields:
Approximation theory: Sometimes it is not possible to get an exact solution to a problem, because this might take too long, or it may not be possible at all. Approximation theory looks at ways to get a solution which is close to the exact one, and which can be obtained faster.
Probability and Statistics: How likely is it that something will happen? - If a coin is flipped 100 times, and lands heads up 53 times, is this coin good for games of chance, or should another one be taken?
Optimization is about finding better solutions to problems.
In ecology certain things are known about populations of animals or plants. This is usually called Population model. Biologists use them to tell how a population changes over time.