A sample that is picked in such a way that every unit in the population is equally likely to be selected in the sample. This ensures that individual units/observations in the sample are independent of each other, assuring a representative sample of the population.
In order to draw a simple random sample from a finite population of size N, one method is to number the population units from 1 to N, then use a table of random numbers or a computer random number generator to select the units into the sample. Or you can write the numbers 1 to N on separate pieces of paper, pool them together and pick the numbers out of a hat to include those units into the sample.
There many types of random sampling:
1. Simple random sampling, used when the population units are all alike
2. Stratified sampling, used when the population consists of natural groups (subpopulations) of units such as males and females, so that independent random samples may be drawn from each group to get a more representative sample.
3. Cluster Sampling, which involves choosing the sample units in groups. For example, if the residents of a city are listed by household, a simple random sample of households is taken and all members of the selected households are included in the sample.
Sampling Overview - American Society for Quality (ASQ) - http://www.asq.org/learn-about-quality/sampling/overview/overview.html