Big Five Personality Traits

The Big Five is a Big Deal because, out of the major personality inventories floating around, it is the only one that was created empirically, as opposed to the Enneagram and the MBTI. Psychological researchers took major adjectives out of the English dictionary, under the assumption that, if people are a certain way, language should eventually reflect that truth. They then had survey-takers sort all those adjectives into different categories, putting in one pile all the words that meant the same thing. It took a lot of math (trade secret: most of psychology is statistics), but eventually psychologists determined that those adjectives fell into 16 categories, which even more math refined into a basic five. Whether the 16-factor model or the 5-factor one is more accurate is still being debated by academic psychologists today.

The Big Five traits provide "an OCEAN of possibility", though we can use a different acronym if that one doesn't float your CANOE. Most of them are Exactly What It Says on the Tin:

Openness to Experience determines an appreciation for variety of experience. A Cloudcuckoolander is likely to score high on Openness, whereas lower scorers prefer the traditional, the obvious and the familiar. It relates also to creativity, appreciation of art and imagination; according to what English-speakers say about themselves, both stem from a single central trait.
Conscientiousness describes how likely someone is to act with self-discipline, responsibility and an interest in achievement. Essentially it describes self-control, from the chaotic and spontaneous people on the low side to the anal-retentive, obsessive-compulsive workaholics on the high side.
Extraversion describes a sense of exuberance and willingness to be involved with the world around them. There is actually a physiological explanation for this phenomenon: there are differences between the brain of an Introvert, which is more likely to be overwhelmed by excess stimulation, and that of an Extrovert, which is more likely to be bored by lack of it. Having said that, the Big Five's version of Extraversion also correlates with energy and positivity.
Agreeableness measures whether you're a Friend to All Living Things or Properly Paranoid. People who score high on Agreeableness are pleasant, cooperative and willing to compromise. People who score low on Agreeableness are suspicious of others' motives and place their own interests first.
Finally, Neuroticism, sometimes called Emotional Instability, measures how well you deal with adversity. People who score high on Neuroticism are easy to knock out of equilibrium; prone to anxiety, depression, stress and so forth; and more likely to overreact to bad news. Low Neuroticism scores indicate stability, calm, and ease at shrugging off negative feelings. This does not mean they feel lots of positive feelings (that's what Extraversion is for); an Introvert with low Neuroticism just doesn't feel much at all.

The Big Five test does not provide "types" that describe all the different combinations. Partially this is because there would be 32 of them and that would be too much work. Partially this is to avoid pigeonholing; what you score is what you score, and psychologists try not to stereotype. Partially it's because, as with the Myers-Briggs, you can score high on one scale but low on another, and a person with high Extraversion and high Openness is not the same as someone with high Extraversion but only some Openness. But mostly it's because the scales don't combine. If you are Extroverted and Disagreeable, that doesn't make you a Grumpy Old Man, because every adjective you can use to describe a human being is already associated with one, and only one, scale. If you are a Grumpy Old Man, it's because being Extroverted or Disagreeable already means being one.

Obviously, this test is not perfect. For one, it was a textual analysis of the English language, and thus might not be valid for speakers of other tongues. (Translations into other languages have met with varying levels of success.) For two, there are a number of traits which the test simply doesn't account for, like Manipulative Bastardry, sense of humor and religiosity. As mentioned, some people still prefer the old 16-Factor theory. And finally, pure general intelligence (the so-called "IQ") seems to correlate with Openness To Experience, which psychologists have flat-out admitted must be a Critical Research Failure. But, again, it's the only personality inventory that was devised by actually inventorying personalities.

Compare The Enneagram and the Myers-Briggs Temperament Indicator.