Randomness is a term that can refer to the condition or state of lacking organization or pattern, essentially being unpredictable. It can also mean an oddness of eccentricity of personality - for example "The woman's interests and behavior had a strange randomness to them."
In research and experimental psychology, random assignment is often used in creating groups of test subjects. This means that subjects are assigned to study groups without any special regard to factors such as age, gender, health, or socioeconomic status. Random assignment assures that no results from the experiment were due to other factors other than the treatment or experimental condition.