Describe what Pearl's actions upon Dimmesdale were and what do you think it means?
The only time Pearl's actions really affect Arthur Dimmesdale in The Scarlet Letter is right at the end when Arthur dies. I assume that's the event to which you're referring. Pearl intuitively knows she has a connection to this man. Each time they meet, there is a moment of drama. She kisses his hand at the Governor's mansion, and she throws thistles at him from the cemetery below his window. In the forest, she washes his kiss from her forehead and the last time they were on the scaffold together she refused to kiss him. This time, things are different.
She understands he has finally claimed her as his own, and she willingly kisses him before he dies. The text says it was if a spell had been broken, We know she goes on to be a loving wife, mother, and daughter. Apparently this moment truly does have a dramatic impact on both of them--he has died with her forgiveness, and she will have a chance to be whole and normal in her relationships with others.