The Big Five personality traits are currently the science preferred mode of studying personality traits. They came to these five traits through statistical analysis.
So, how does this work? It works based on the lexical hypothesis, which claims that any to-human important characteristic of the world in encoded in the human speech. So any important differences in the human personality would have a way to be expressed in the human language.
As somebody who also dabbles in the experimental phenomenology, I could context to this hypothesis, but I do believe that quite a lot of variation in human behavior is captured in the words that we use.
So, what the scientist did was to take all the words in the language that can describe a human's trait. So that would be words like nice, slovenly, hard-working, beautiful, intelligent,... In most case, because of the practical reasons, they only take the most frequent x words, where x is a number.
Then they give these words to people and tell them to rate themselves on the scale. So, foe example, I would rate myself high on intelligence, but low on social and so on. Then they used something called the factor analysis to see if there are some words that exhibit the same patter of change. One of that pattern would be, that people that describe themselves high on happy, will most likely also describe themselves high on smiling.
Usually, there are five patterns of words that come there:
First is extroversion. People that are high on extroversion are energetic, social, risk-taking, hedonistic, positive, assertive, dominant, uplifting and so on. There are the people that needs to be with other people and need to have something happening to them all the time.
The second is neuroticism. People that are high on neuroticism are negative, feel a lot of negative emotions, are fearful, nervous, sad, tense and anxious. These people see the danger in everything and want to be prepared for every eventual disaster.
The third is conscientiousness. People that are high on consciousnesses are hardworking, controlled, traditional, obedient, organized and so on. These people are usually these workaholics, that are miserable when they are stopped from doing the work.
The forth is agreeableness. People high in agreeableness are high in compassion, prosocial, altruistic, modest, prefer harmony, put other people in front of themselves and so on. These people are nice to talk to and they are the ones always willing to help in any way they can. They make people feel nice.
The fifth and last in openness. People high in openness are people that are original, com up with new ideas, question status quo, enjoy intellectual simulation and appreciate beauty.
Rearranging the first letters of these traits gives the acronym OCEAN.
People are then like the symphony of different notes that are the results of different traits. So, I am low on extroversion and agreeableness, so my song is going to not have extroverted and agreeableness notes, but will instead have introverted and disagreeable. In comparison, my openness is relatively high, so there are going to be a lot of openness notes in my music.
Other people would have different music. Some would be high extroversion and high agreeableness, or maybe all of the traits are middle ground, sometimes more expressed and sometimes less.
These traits also have a sub-traits, but while the five traits are quite accepted, there are a lot of different sub-traits divisions. Also, there are super-traits, where the extroversion, openness and neuroticism are grouped together and the agreeableness and conscientiousness are grouped together. Some people call them the plasticity and stability traits, but I have also seen them being called simply alpha and beta.
But these five traits can help with evaluation other people and are another useful tool for understanding people.