"Furtive" comes from the Latin word for "thief." When you do things furtively, you do them like a thief: quickly, sneakily, and secretively, so that nobody sees you.
In other words, furtive people and movements are fast and sneaky.
You might take a furtive peek at someone: a quick peek, then a quick look away before anyone notices you've peeked. Or you might give your friend a furtive smile: a quick, secret smile, before anyone else notices.
You might slip furtively down to the refrigerator late at night to get a snack, without anyone hearing you. You might reach furtively for your phone to play a game during a boring class. Or you might take a furtive glance at a friend's test paper. Hey! Eyes on your own work!
"Furtive" is a formal word, like "sly" and "stealthy." You're not likely to use this word when you're chatting with friends. But if you're writing an essay or a story, then go ahead and write about furtive people who cast furtive glances at each other, laugh furtively behind their hands, and sneak furtively into places they shouldn't be.