In an experiment, researchers attempt to control as many variables as possible with the goal of determining the effect that one variable has. Researchers conducting experimental research manipulate a single variable to determine its effect. An experiment has both an independent variable and a dependent variable. The independent variable is the thing that the researchers are manipulating. The dependent variable is what the independent variable affects. For example, researchers studying the effects of smoking in lab mice might introduce different levels of cigarette smoke to groups of mice. The smoke is the independent variable, and the effect the smoke has on the mice is the dependent variable. The dependent variable is what experimental research measures.
Researchers doing observational studies don't manipulate variables to attempt to produce results. Instead, they simply watch what happens. They might have a particular group or thing they want to study, but an observational researcher has to find that group or the thing he wants to study occurring naturally. For example, an observational researcher studying the effects of smoking would look for people who smoke and people who don't smoke, and compare the two groups to each other, rather than introduce smoking to a group of people who had never smoked before.
The key difference between observational and experimental research is the type of relationship that each can establish. Observational studies show correlations, while experimental research shows causation. Correlations show that some type of relationship exists between two things. For example, "People who smoke are more likely to have liver cancer" is a statement of correlation. A causal relationship indicates that one thing causes another. For example, "Smoking causes liver cancer" is a statement of causation.
Both observational studies and experiments have their limitations. Many experiments that would be able to prove a causal relationship would also be unethical to perform. For example, researchers may not do an experiment to see if smoking gives humans cancer by taking a group of people and forcing them to start smoking. Researchers can use observational research in situations when the same study would unethical in experimental research; however, the results of observational research aren't always clear, and are more open to interpretation.