To look on enviously or helplessly while doing nothing; literally to hold a finger in one's mouth, but commonly used idiomatically for passive onlookers.
友だちが昇進するのを指をくわえて見ているだけだった。
I just watched enviously while my friend got promoted.
子どもがショーケースのケーキを見て指を咥えている。
The child is holding a finger in his mouth while looking at the cakes in the display case.
彼は本当は手伝いたかったが、結局指をくわえて見ているしかなかった。
He really wanted to help, but in the end he could only stand by helplessly.