Think about all the things you've ever learned in your life.
You've never learned anything you didn't want to learn.
You only learned the things you wanted to learn.
That may sound extreme, but it's true. Anything you've ever learned, you've learned because you chose to.
You learned to walk as an infant because you wanted to get places without being carried. You learned to read because you wanted to know what was in the books you saw other people reading. Every toddler in the world learns to work the remote control with no formal schooling whatsoever. Why? Because they don't want to be stuck watching their siblings' favorite shows forever. They want to watch what they want to watch.
"But wait: I didn't want to learn how to do my taxes!"
Of course you did. You had an intense desire to avoid prison. (If that's not true, I don't know how to talk to you about much of anything.)
It turns out that we learn some things not because we are curious about the things themselves, but because they are connected to other things we desire or are curious about.
To avoid prison, you had to pay taxes. To pay taxes, you had to learn how to file them properly.
You may not necessarily want to learn to type quickly or code a website. But if you are interested in becoming a blogger, being able to get your thoughts on the screen as quickly as possible, in the style you desire, may drive you to learn those secondary skills.
Sometimes wants are in conflict. When wants conflict, a choice is required.
For some taxpayers, their desire to hang on to their time and money isn't as strong as their desire to properly file taxes; those taxpayers pay an accountant to file their taxes. For some bloggers, their desire to have a website look perfect isn't as strong as their desire to save money and time; those bloggers settle for less-than-perfect websites.
Those are perfectly valid choices.
What does this have to do with the classroom?
First, you have to honor the choices your students make, as much as possible.
Beyond that, it's simple. If you want students to effectively learn something, you have to connect it to their innate curiosity - their inner will to learn the things that interest them. You have to create a scenario that increases the likelihood of their natural curiosity leading them to the choice you want them to make. That's easy if you're teaching really young children; they're naturally curious about almost everything.
However, as students age and develop personalities, they naturally become less interested in some classes, and more interested in others. If you teach chemistry, the kids in your class who are interested in becoming doctors probably aren't terribly difficult to motivate. If you teach English, the kids who start each day reading their favorite news blog probably lock in pretty well.
What about the others?
It's easy to teach English to kids that like to read; it's easy to teach math to kids that like to solve puzzles. But how do you engage a student who just isn't curious at all about your subject?
First of all, it's perfectly fine. There's a reason you became a history teacher instead of an accountant: because you were more interested in history. So what do you do in the classroom for students that don't care about your subject?
I can't answer that question in a way that will work every time, but here are some potential questions you want them to be asking themselves:
What is it like to be a person who can converse intelligently about most topics?
What is it like to be prepared for the ACT?
What is it like to legitimately have all college / career options open?
What is it like to not worry about my grades?
What is it like to impress my parents with something I learned at school?
What would it be like to never have to worry about money?
What would it be like to be the smartest person in a room?
What would it be like to not be scared by my next test?
What would it be like to think of myself as a wise person?