A personality is the unique combination of qualities that make up an individual's distinctive nature. A well-developed personality is a very important thing for a fictional character to have if they're going to be three-dimensional and interesting instead of flat and dull.
Some key aspects of personality include, but are certainly not limited to: basic outlook on life, passions, goals, hobbies, likes and dislikes, sexuality, sense of humor, morality and ethics, attitude toward religion/spirituality, level of introversion/extroversion, ability to relate to others, emotional maturity, mental stability, and level of intelligence.
Aspects of personality notably do not include physical appearance and abilities, although these may certainly be used to implicitly indicate things about a character's sense of style, competitive spirit, upbringing, etc.
A well-developed personality should take into account the character's backstory, their present motivations, and their goals for the future. Our past experiences shape who we are, whether we embrace them or reject them. They give us the framework we use to make decisions in the day-to-day, most of which will have to do with immediate wants and needs. However, a person's long-term goals also influence their decision-making, and are therefore important to consider—including whether or not the character is the type to sacrifice short-term gratification in favor of long-term rewards.
Bit characters and Mary Sues are noted for not possessing much in the way of personality. In the case of a bit character, this is usually because they have only a small role in the story and don't have enough screen time to develop. Given a chance, they can usually become proper characters. Many PPC agents are former bit characters recruited from badfic.
Mary Sues, on the other hand, suffer from bad characterization. They tend to be selfish, shallow, and only focused on their immediate goals, even if their stories claim they're angelic saints who routinely kiss the baby and pet the dog. Their abilities don't reflect their stated backstory, and their decision-making processes are inscrutable to anyone with an understanding of basic human psychology. This is a very important factor in telling a Mary Sue from a good original character.