Slippery things are slimy or wet, or for some other reason cause you to slide on them. A slippery fish is hard to hold in your hand, and a slippery path is easy to slip on.
You should drive slowly and cautiously when the road is slippery after it starts to sleet. And your hands may get slippery with sweat when you're nervous about a job interview. You can also use this adjective in a figurative way, to mean "tricky" or "unreliable," so you might complain about your slippery brother, who always manages to disappear right before it's time to take the trash out or load the dishwasher.