Reasons we care:
*We care about a character because their issue mirrors something of our own life, thus a connection is made.
*The character has a goal that we deem worthy or noble.
*We see something in them the other characters do not see, pressing us to cheer for them.
*Sympathy for the character has been stirred because we know what they have experienced/endured (through well-laid snippets of backstory).
*Their goals and attitudes are similar to our own.
Unlike life, reading gives us the opportunity to not only see a characters reaction, but understand the basis for it. This is important to understand. In real life, we want others to judge us not by our actions but by our motives. The problem is life doesn’t afford the ability to explain our motive before we propagate a reaction that can be viewed negatively by others.
Now really think that through. It's a lot to comprehend. Perhaps an example will help.
Character A just screamed at her eight year old child for tripping and tearing a hole in the knee of her new pants. Viewed by a stranger in real life, Character A’s reaction to the child would be a big negative and there would be no second chances for Character A to redeem herself. How dare that woman scream at that poor kid. But in story, if we need to draw sympathy for the character in order to build a connection with the reader we simply show the course of her day. She just got fired and returned home early to find her husband in bed with another woman. Then, after crying and packing her husband out the door, her child’s bus pulls up ten minutes earlier than expected. . . Under these circumstances we can better come to terms with the reason why Character A might lash out at the child.
So writing as a whole allows us unique opportunity to create a character that we are sure will connect with our intended audience. We must learn how to manipulate information and interaction within a scene to show the best and justify the worst traits of our protagonists. And then, according to how many main characters you have, do this again for each of them. Easy-peasy, right?