What does the hourglass emoji mean on Snapchat, and how do I get rid of it?

The hourglass means your Snapstreak with that person is about to end. A streak (the fire emoji with a number) counts consecutive days you've both sent snaps, and the hourglass warns the 24-hour window is nearly up. To save it, you and that friend each need to send an actual SNAP (a photo or video, not a chat message or a Story) before the timer runs out. Chats, texts and Memories don't count, it has to be a direct snap both ways. If it disappears without the streak ending, you made it. Snapchat doesn't say exactly how long the hourglass lasts, but it usually shows in the final few hours.

Only a real snap (photo or video sent directly to them) resets it, texting in the chat does nothing, and both people have to send one. That's why streaks die even when you 'talked' all day in chat.