This is the 2349th most frequent Chinese word.
偷偷
"Secretly" or "stealthily."
The word '偷偷' here is used to indicate that the action (walking into the room) is done stealthily or quietly to avoid being noticed.
他偷偷地走进了房间。
He sneaked into the room.
In this sentence, '偷偷' describes the kitten's sneaky and unnoticed action of taking the fish.
小猫偷偷地从桌子上拿走了一块鱼肉。
The kitten secretly took a piece of fish from the table.
Here, '偷偷' conveys that the action of checking was done in a surreptitious and private manner.