Dependent variables are observable phenomena which are influenced by other phenomena. In an example, for someone studying how much light impacts the growth rate of plants, growth rate is the dependent variable, because it depends on how much light the plants receive. When people design experiments, they identify the dependent variable or dependent variables at the start, so that they can measure them throughout the experiment. They also identify all of the factors which can influence the dependent variable, to the best of their ability.
These variables could be thought of as having values which are dependent on manipulation of something else. This "something else" is known as an independent variable. Independent variables can have an impact on dependent variables, but they do not change in response to other variables in the experiment. Instead, they are manipulated by the experimenter, with the experimenter using controlled manipulation to test predictions about how changes in the independent variable will alter the dependent variable or variables in the experiment.
Dependent and independent variables turn up in a wide variety of locations. For example, the value of the stock market is a dependent variable because it is influenced by external factors. In scientific experiments, dependent variables are the things which people are trying to study and measure. When designing experiments, researchers try to think about all of the things which can influence the things they are trying to measure, so that they can control the environment of the experiment as much as possible.
In our plant example above, growth rate is a dependent variable, but so are things like when the plant leafs out, whether or not it flowers, and so forth. In this case, multiple dependent variables can be altered by manipulating the independent variable. Not giving the plant enough light may slow the growth rate, while giving it too much light may result in burned or damaged leaf buds, preventing the plant from leafing out.
People can identify dependent and independent variables in areas such as statistical analysis, as well, looking at things which appear to be linked and exploring the ways in which they are linked. However, some caution is advised here. Correlation is not causation, and when doing statistical analysis, people should avoid the temptation to simplify or manipulate the information to meet a specific goal. A good analysis will stand on its own, and readers should agree with the way the researcher identified dependent and independent variables.