Creating a sense of purpose isn't easy, and depends on numerous factors and questions whose answers can change with every new scene. All of these elements come together in each scene to move the character forward through the story, and create a sense of investment that makes the viewer identify with them as entities. For example:
What does your character want?
Knowing this is key to telling any story, and creates the driving impetus that propels us from beginning to end. If you're telling a story in multiple scenes, you may have to define both an overall goal for the full-length animation, and a goal for each scene, but there should still be a goal in mind with every action portrayed.
Do your character's actions reflect pursuit of their goal?
There's a sense that we have to always show characters moving, whether they're doing anything relevant to the scene or not. But if their actions aren't relevant to the scene, why are they in the scene at all? Everything a character does should convey what they want. This can be subtle: someone is standing at the bus stop waiting for the bus, so they're whistling, checking their watch, glancing around, kicking their feet, all to show that they're waiting and they want the bus to arrive. Variations on this action can convey the intensity of their desire; they could frown, mutter, stomp, showing impatience. Or they could watch butterflies, sigh, look for shapes in clouds, indicating they're in no real hurry and are daydreaming while they wait for their end goal to arrive. For a more high-intensity example, a character fighting for their life should only portray actions relevant to the battle. The pretty, whipping hair swirling everywhere is less important than the lock of sword to sword, the strain of muscles that indicate the desperate strength funneled into their want to stay alive.
Why is your character doing this?
You've heard the joke about diva actors refusing to perform until the director answers the classic question: "What's my motivation?" You may not realize it, but your characters are asking this as well. If every action reflects a goal, why are they pursuing this goal? Is the person waiting for the bus in a hurry to get home? Is the person fighting for his life desperate to defeat the enemy and save a comrade? We need to feel that this goal is important to them, to impart that sense of purpose that's so important.
Do your character's emotional cues convey their desires?
Get your mind out of the gutter and take a look at how you convey emotion in your character actions, whether through expression, posture, action, and any combination of all three. Ask yourself how they feel about the purpose they're accomplishing in the scene, and make sure it's conveyed in every emotional cue the characters give. This even works for the stoic type who don't show emotion; there are still ways to use body language and behavior to reflect their focus on achieving what they want, and often the attempts to repress emotion are more telling than the blatant displays. A subtle tightening of the mouth while speaking can convey volumes.
What is your character thinking during the scene?
Thought drives purpose - so while all these things are going on, what's going on in your character's mind? Does the way you've chosen to portray their actions reflect the wheels turning in their head? This can tie into emotional cues, basically showing their response to the ideas, concerns, and conclusions in their mind along with their response to external stimuli. Following a character on their journey of reasoning and understanding, even when it's wordless and conveyed only through gesture and expression, and deepen engagement.
Combining all these elements with finesse to balance them into a nuanced character portrayal is how a rock becomes a person, and a person becomes real - rather than just lines squiggling across the screen, a mere illusion of life. Always animate with purpose, and use that purpose to make us believe the fictional people you create are entirely too real.