This is a hard question to answer. A lot of the games I've played over the years, the stakes have been world-saving, which makes them pretty important! But the stakes should matter even when they aren't so big.
I guess some of it comes down to the degree the players have invested themselves in the world. It's pretty easy to have even minor stakes feel important to me: give an NPC I care about a good, in-character reason for caring, and my character will too - and "care about" can mean my character loathes them; there's a lot Svetlana would happily do if it meant undermining Irrevetti's power. While Lacy had to point out to other party members that saving his friend's friend would help us achieve our meta-goal of saving the world, for Solomon it was enough that someone she admires asked for her help.
Another trick is to look at the character - both the character sheet, and the way it's played. In Deadlands, my partner knew Carson would offer himself as the one who'll die when we attempt to bring the Flood to Lost Angels because the character has the "Big Damn Hero" flaw (or whatever it's actually called), and the player remembers it too. Likewise, Solomon would do whatever he needed her to to assist, because she's Loyal. Taji is overconfident and very competitive, so give her a challenge or imply she can't do something and she'll go out of her way to prove you wrong: the stakes aren't particularly high, necessarily ("bet I can dig faster than you!"), but they'll matter to her (this also works on Bells's Mage character, Howard, who is also overconfident and dislikes admitting he can't do something). My new Exalted character Amaryllis, whom you haven't met yet, has very high Compassion, which means give her a bit of a sob story and it becomes important.
Make it personal. NPC's are the easiest way for me, but not all players are interested in NPC's, so maybe have a beloved item nicked from one of them, or rumours of an item of power another would benefit from. Feels a bit boring to me, but works for many other people.
Remind players of clocks ticking - that plague village they visited a while back, has anyone been back to see if it's still spreading? That Quantum lake that covers Vienna, when did you last visit? It occurs to you you haven't seen Tark for a while. A newspaper headline announces the progress of the army marching this way (I love in-game newspapers for delivering plot hooks and clock reminders). You turn on the radio to hear Theresa's parents pleading for her safe return. You did remember to write back to Marcy, right?
If you're taking part this year, don't forget to link to your response in the comments below!