Sample size is important when researching the results of a scientific study or designing an experiment. One wants a sample size to apply to the entire world or universe, but in practice its impossible. So, typically a sample size will be made up of enough data to be statistically relevant which then can be applied in practice.
What can happen if a sample size is too small? - Data can be skewed towards a particular positive or negative result without any real applicable statistical significance.
Example: Ten people take a new pill to relieve their back pain and 3 people get better and 7 don't. Another ten people take a placebo for their back pain and two get better. The actual medicine has a ten percent effectiveness rate over placebo. One would consider this to be an effective drug over the placebo but look at the sample size for the experiment, there were a total of twenty people in the experiment. People who declare back pain as a regular symptom in their daily life are much more numerous than just twenty people in one experiment. When this data would be statistically analyzed, it would be found to have a high variance. A high variance is bad for the results of an experiment.