So what are the basic elements of a great character? Getting to understand how they think is primary. Readers want to be able to predict the reactions of characters (and then be surprised when they do the unexpected) based on their personal issues, inner dialogue, and the context that you present them in. They want to know if the character is brave or shy or fragile or clever or introverted or an adrenaline junkie. Will they choose adventure (yay!)? Are they likely to figure out the mystery or survive a cross-country trek? Are they afraid of bugs? When buggy looking aliens invade, will our hero be constantly nauseous? Knowing how the character (robot, dog, woman, tree, child or paladin) thinks gives readers insight, and insight makes people feel powerful. Now they're hooked.
But predictability and character growth is only half the battle. You need to bridge the distance between writers and readers to give them what they really crave. Whatever their foibles and talents, characters make their way into our hearts as we join them in the great escapade of (fictional) life. Harry Potter is endearing because he's bullied. Romeo falls in love so deeply he can't think straight. Ever been there? If you haven't, perhaps you will, and then BAM! All that crazy makes sense.
Having a plot that brings your multi-dimensional character along a literary journey that is fun and engaging brings the reader into your world. Your character is center stage, but you have to dress up the stage, create the world. Your agenda (plot) is what makes your characters pop. Some fit in perfectly, like David Copperfield in Dickensian England. Some are aberrant, such as Scarlet in Gone With the Wind. Either way, the reader will remember your characters because the story in which they find themselves provokes emotion, entertains, and brings the character traits and the journey together in a landscape that allows your protagonist to come alive, even if just for a while.