Background: Every character has had a life before the beginning of the story. The things that have happened to them and the things they have done have all contributed to the person they are now. Most of their background won't make it into the story, but you need to know all of it. You never know what sorts of things will influence a reaction to a crisis.
Present: Every character also needs a full life that they're living in the present. They have work, leisure, friends, frenemies and enemies. They have political opinions and morals and values. They have people in their lives that they love, and ones they hate. No person is an island, isolated and just waiting to be filled with purpose during the course of your story. They already have a purpose; it might not be the one they really want.
GMC (Goal, Motivation, Conflict): This is one of the difficult things to do. Every character has both internal GMC and external GMC. The internal GMC is influenced by their background. External GMC arises from their present and who is in their life right now. A character can have more than one internal GMC and more than one external GMC, but there must be one of each that have to be fulfilled for your character to feel they've reached the point in their life where they've realised their potential and can be happy.
You might have noticed I haven't mentioned physical appearance. To me, that isn't so important. It's also something that's going to be influenced by the other things. For example, if your character's present includes being an active member at a gym, then s/her is going to have a certain type of physique. If their past was violent (domestica abuse, military, etc), they'll probably have scars. Let their appearance grow out of their experiences, then add the superficial pieces like hair and eye colour.
Over the next few weeks, I'll look more closely at each of these things and share with you some of the things I do to build my characters.