As Ariel said, "vanity" concerns excessive pride about personal appearance and "conceit" is more about excessive pride regarding personal traits like intelligence or personality features. "Hubris", however, has its own specific connotation in terms of excessive pride: "Hubris" is such an excessive amount of pride that it's considered, or becomes, a "fatal flaw." Hubris is a level of pride that blinds someone to their actual strengths and weaknesses, and makes them unaware of how the people around them actually feel. That "fatal flaw" can be literally fatal (as in the assassination of Caesar because he ignored warnings that he had many enemies), or can lead to massive mistakes in judgement that can ruin relationships and careers. This complex of hidden meanings behind the word "hubris" is a large part of the reason why it's not commonly used; the word is very situational. "Vanity" has the connotation of causing a person's personality to be very "shallow" because appearances are all that matter to them. "Arrogance" is a very general descriptor that's relatively synonymous with "conceit" but is used much more frequently, at least in spoken English.