If we accept fiction as the exploration of ideas, theme is the central idea explored in a story. It often involves the intersection of conflicting ideas.
Most themes emerge organically as a story is written and are developed further in editing and revision. Good drama gives rise to a theme naturally--conflicting forces engaged in a struggle. Those characters and struggles often boil down to simple ideas: peace, violence, opportunity, revenge, tyranny, desire, arrogance, etc. Going back, a writer might start to notice these themes and do things--small or large--to enhance them.
Some writers start with the theme and build a story around it, selecting characters and conflicts that will investigate the theme from every angle. To do that, one needs to develop characters and conflicts that highlight that theme in the best way possible. They have a huge gallery in the beginning, so they need to be adept at narrowing the choices and focusing their ideas.
The theme of The Superhero Murders might be law vs. vigilantism but I've found it's really an exploration of violence in a lawful society. To explore that theme, I've developed a lawful character and a vigilante character--easy enough, right? But that hardly explores the theme, so I have a character that aspires to vigilantism but never engages in it, a character that has given up on justice and humanity altogether, a character that walks a line between the two because of the situation I've put her in--that's Kim, the main character--and lastly I have the antagonist, a fellow that uses violence to achieve a twisted goal. He preaches law, but it's his own version of law. He strives for a goal that is insane to everyone else.
I began with a character, as many stories do. The theme and ideas came later. As I reworked and reworked (and reworked) the story, the theme grew stronger. Along the way, I continually thought the theme was vigilantism. Only recently did I realize that the large theme is violence within society. (e.g., do the police enforce the law through respect or through fear of violence?)
My thoughts: to explore theme, the writer needs at a minimum:
SIDE NOTE: Symbolisms and Motifs are related. In On Writing, Stephen King mentions that he eventually noticed that blood was a recurring symbol in Carrie. It appears in each major plot point. He then built that motif up during revision. (Now, a motif, a recurring symbol isn't the same as a theme--but it's a cousin, and this illustrates how such things as tone, symbolism, motif and theme can all emerge in revision.)
It's not required that a character be likable--sometimes we want them to be hated, but not always. Authors often discuss what makes a character likable, or even just worthy of sympathy.
Here's my list.
The character possess some trait or goal that is admirable. She has a noble goal or an inspiring quality. She does things we can respect and aspire to. It can even be simple: a man wants to provide for his family. A mother wants to comfort a child from the horrors of the outside world. Consider how much more those appeal than a man who just wants loads of cash and power.
The familiar character is one we can identify with. She wants something we want. She does things the way we would do them. She thinks in a way we recognize. In literature, the familiar provides validation. This is why the everyday hero is so popular in literature. He's one of us.
If a young boy tries to avoid the school bully, we can understand his actions because we've all faced bullies of some kind of another. We may not identify with a knight fighting a dragon, but when the village sweetheart makes him stammer and sweat, we feel like we understand. (And we might have even admired his bravery in that fight.)
We can just call this drama for short, but some personal definition is required here. By drama, I mean the character suffers and struggles. Something is wrong, something has been taken away, something awful has befallen our character--that alone inspires sympathy, a necessary ingredient, but that alone can fall flat unless the character gets up and does something about it. She tries to find balance, contentment and happiness again. If a man is abducted by slavers, we feel bad for him, but if he never fights for his freedom, how much of a story do we have?
(The struggle part could easily be slipped into the "admirable" category, and I considered that for some time, but I personally felt it is important enough to stand apart with suffering in the drama category.)
Writer of speculative fiction. Current work in progress is an untitled dark fantasy novella.