Choice is an incredibly important part of RPGs, and how its handled can tell you a lot about the game and its priorities. But choice is also a tricky widget, one of those things that looks simple on the surface, but offers great complexity as you delve in deeper.
For example, there are different kinds of choices. One model I'm fond of it to look at the bulk of choices as existing on two axes.
The first is whether or not the choice is real. A real choice can be a little bit difficult to define in the context of an RPG because, on some level, it's all fiction. Still, the idea is this: a choice which has an impact on the fiction (that is to say, it causes a change). Now, for this to make sense you need to buy into the idea that the idea of the game has some concrete reality, and not everyone is on board with this idea, but let's just roll with it for the time being.
This question comes up a lot in discussion of stories in games. In a game where the plot finds the players, you can often end up with false choices. For example, the players may be presented with a map with numerous destinations and may apparently choose from any of them in their hunt for the MacGuffin. In some games, the next clue the players need will be in whichever destination they choose. This works out nicely for the ebb and flow of play, but it also means the player's choice didn't actually have any impact on the game.
The counterpoint is pretty obvious - player choices that direct play or impact the setting. These are the bread and butter of solid tactical and resource management play - action is taken, it has consequences, those consequences are responded to with further action.
This is a good division, but to really give it context, how to make it so hinges on the second axis, meaning.
Meaningful choices are ones where the players have a personal investment in the outcome. Ideally, this is derived from their investment in the game and its elements, but the source is of secondary importance. Players may make any number of choices for their character, but some of them are simply trivial, like what they had for breakfast. They might be colorful or entertaining but, the player doesn't have an emotional investment in the outcome. A choice that affects things that are important to the player is going to carry more weight, but pinnign that down can me rough.
This is where the axes start helping. The easy assumption is that meaningful choices just needs to be about something important, but that overlooks something critical. See, no matter how high the stakes are, they only matter if the choice is not obvious (which is to say, that there's a real choice). If the choice is between saving 100 and 1000 lives, it has no weight because, however important those lives may be, the choice is obvious. Even when you sweeten the pot and, say, put loved ones in the 100 that can still fall flat in the kind of game that rewards "right" decisions.
Because of this, meaningful choices can't be strictly utilitarian, cost-benefit analysis stuff. If everything important in the equation can be boiled down to math then the choice is not made, it's discovered via calculation. This can be a satisfying process, but it scratches a very different itch.
And that leads to the other end of the axis - sometimes you don't want to be getting squishy stuff all over your wargame. Tactical decisions and resource management are routes to fun, and if you're looking to capture that particular kind of play, adding in emotional meaning to the game is going to undercut things. Even if one doesn't want to be in this mode all the time, there are times when you don't want to have emotional investment in the soldiers in your wargame.
Given all that, I like to view the upper right hand corner as a goal, even if its not always practical. Sure, every choice should be real and meaningful, but every now and again I'm going to want to step towards something real but uncompelling (like a good fight scene for its own sake) or meaningful but perhaps a bit less real (that is to say, something fuzzy and muddled like most human interactionis). Hell, sometimes I want to dip back into the trivial just for the sheer joy of playing through eating my breakfast. But what's important is that I know my target square. Someone else might have a different target square but still dip into the others based on their own needs.
1 - I uploaded a diagram here, but Google is being weird, so it may never show up, so in its absence, let's illustrate with a dungeon room with two doors.
In a game with fake, meaningless choices, there's a monster behind each door which you will fight solely because its a monster. In some cases, one door will be locked in a totally unopenable fashion.
In a game with real, meaningless choices, one door has a monster and the other may have four hours of boredom (or a bathroom, or some other non-monster option) behind it. Whichever door the players choose is the one they're stuck with.
In a game with fake, meaningful choices, the bad guy that the players REALLY want to fight is behind whichever door they open first.
In a game with real, meaningful choices, the guy they hate is behind one door, but Aunt May's medicine is behind the other one.
2 - One alternate version of this is that whatever choice the players make, they will still end up in the same place due to events the GM brings to bear. Net result is pretty much the same.
3 - Obscuring information is the common way to address this, so that there's math, but you don't know what it is, so you have to guess, and in guessing you theoretically make it a softer decision.
4 - Much the same way that you don't necessarily want to bust out a social combat system every time you have a scene with a loved one.