The "Big Five" personality traits are five empirically supported dimensions of personality -- Openness, Conscientiousness, Extroversion, Agreeableness, and Neuroticism (OCEAN, or CANOE if rearranged). This description is also known as the Five Factor Model (FFM). The Five Factor Model of personality traits was first presented by the president of the American Psychological Association, L.L. Thurstone, in 1933. Each factor is actually a cluster of more specific traits that are known to be statistically correlated. There is the most disagreement about the specifics of the trait of Openness.
The Five Factor Model of personality traits is meant to be descriptive (objectively presenting the data) rather than theoretical -- it does not attempt to explain why these traits are clustered and distinct. Many have attempted theories to explain it, but there is not full consensus on any one theory. To summarize what the personality traits mean:
Openness: appreciation for emotion, art, unusual ideas, adventure, curiosity, imagination, and variety of experience.
Conscientiousness: a tendency to act dutifully, show self-discipline, and aim for achievement; planned rather than spontaneous behavior.
Extraversion: positive emotions, energy, self-confidence, outgoingness, and the tendency to seek stimulation and the comfort of others.
Agreeableness: a tendency to be cooperative and compassionate rather than antagonistic and suspicious towards others.
Neuroticism: a tendency to experience negative emotions easily, such as depression, anxiety, anger, or vulnerability; sometimes called emotional stability.
When these values are scored via tests, the results are usually given in percentile format. As in, I might be in the 90th percentile for Openness, but only the 50th percentile for Conscientiousness. These personality traits are not absolute, but do persist when all else is equal.
The Five Factor Model was created using lexical analysis -- analyzing 17,953 personality-describing words, which were reduced to 4,504 adjectives, then just 171, through the elimination of synonyms and near-synonyms. In the 1940s, 16 major factors were isolated and considered the most important, and in 1961, it was trimmed down to just five. After two decades of a haitus in research, the Five Factor Model was revived in a conference in 1981 where a group of prominent personality researchers agreed that it was the most empirically accurate and predictive model available. Since the early 1980s, the Five Factor Model has been considered the most scientific of the personality tests, in contrast to, say, the Myers-Briggs Type Indicator (MBTI), which is based on discredited typological theories of Carl Jung.
