A vivid character will progress the story by him/herself instead of having the author unfold it. To write a vivid character, you need to find their personality through their: motivation, fear, like/dislike, and surrounding characters.
By setting a few dislikes and likes for your character, it helps you find out more about your own character, physically and mentally. Ex: If he or she likes sport, maybe he/she is more athletic and agile, and these skills come to play in certain event, that maybe even you didn’t intend it to before.
There should always be someone who help drive your character to progress forward and grow: friend, family, rivals or nemesis. Unlike in backstory, the friends and family here helps mold who she/he is going to be and not be. His/her connections with other characters influences who he/she wants to be.
Fear will force your character to choose a path he/she isn’t ready for or doesn’t want. Fear also shows emotion, human nature and makes characters feel real.
This is a lot like purpose, but more on an emotional and mental side of things. All character needs something that makes him/her want to move forward. Motivation can be either long-term or short. It can just be there to help your character to the next arc or to the end of the story.