Break, break, break, On thy cold gray stones, O Sea! And I would that my tongue could utter The thoughts that arise in me.
The speaker addresses the ocean directly, telling the waves to "break, break, break" onto the stony shore.
After telling the sea to keep doing its thing, the speaker regrets that he can't express his thoughts.
He doesn't come out and say, "I can't utter/ the thoughts," he says that his "tongue" can't "utter" them. This makes him seem kind of passive – he's not speaking, his "tongue" is doing it.
He's not really thinking, either – the thoughts "arise in" him almost spontaneously, without effort.