If something is stoppered, it means it has a stopper or cork put in it to close it.
Stoppered things are usually closed and safe from spilling or leaking.
Examples:
The bottle is stoppered with a cork.
She stoppered the test tube to keep the liquid inside.
The stoppered jar won't let any air in.
The stoppered flask won't let the magic potion out!
The stoppered bottle held the genie inside.
The stoppered jug kept the treasure safe.