What does Pearl want from Dimmesdale? In chapter 22.

Pearl wanted a public kiss....

"I could not be sure that it was he; so strange he looked," continued the child. "Else I would have run to him, and bid him kiss me now, before all the people; even as he did yonder among the dark old trees. What would the minister have said, mother? Would he have clapped his hand over his heart, and scowled on me, and bid me begone?"

"What should he say, Pearl," answered Hester, "save that it was no time to kiss, and that kisses are not to be given in the market-place? Well for thee, foolish child, that thou didst not speak to him!"