I frequently remind animation students to always think about these questions when animating a character. It is really important to know who your character is when working on a shot and to know what happened before and what is going to happen afterwards. The character's current situation and state of mind will determine what choices your character will make and therefore dictate to some extent what your acting choices should be. By that, I mean you have to think beyond the mechanics and physics of your animation. Of course, as you start learning the principles of animation, you're more concerned about making your animation look right, to avoid any pops or floaty movements, and that's understandable. But hopefully you will also start to think about WHY your character is doing something, and not just HOW.
I remember watching an episode of Inside the Actor's Studio and the guest mentioned something very interesting that stuck with me ever since. Imagine these two situations: one, you're coming home and you're going to bed. Two, you're going to a hotel and you're going to bed. Technically both objectives are the same. But at home you're familiar with the surrounding, you know where what is and you've done this procedure many times. At the hotel you enter your room for the first time and you need to figure out where what is and you're generally thinking more about your actions. So, to be specific, you enter your house and throw your keys onto the same table as always. Since you've done this many times before, you don't even have look at where you throw the keys. You're mentally one step ahead, so your movements are fluid, casual, etc. At the hotel, you might look around first in order to figure out where you'll put the keys down and do the same in order to get undressed and to brush your teeth. Your movements will be more hesitant and distinct. That approach was really interesting to me and made total sense once I thought about it.
Now on top of that, throw a specific state of mind in there. Is your character tired after a trip, or grumpy, happy to be home, drunk, or is he/she a fugitive, hurrying, etc.? The way a character feels will influence your acting choices and the same goes for his/her surrounding. So when you have a thief robbing a museum as a shot for instance, is the thief super confident or nervous, does he have to hurry? And so on. It's much more interesting to come up with acting choices once you're thinking a bit more about who your character is and why he's doing what he's doing.