Fetching details from the dictionary...

to adhere to; to stick to; to cling to
to keep close to; to go along with
to get involved with; to be thick with; to become intimate
食べていた飴が歯にくっついてなかなか取れない。
The candy stuck to my teeth and won't come off.
彼女はずっと彼にくっついていた。
She kept sticking close to him.
子供が貼ったシールが壁にしっかりくっついている。
The sticker is stuck to the wall.