Literally, when the speaker tells the sea to "Break, break, break / At the foot of thy crags," he is ordering the sea to go ahead and crash into the rocks at the base of the land, perhaps the land on which he stands. The "thy" to which he speaks is the sea, and this is a technique called apostrophe, when the speaker addresses something that cannot respond as though it could. However, this "break[ing]"—including the repetition of the word "break" three times—is juxtaposed with the next, intangible, and much softer idea: "the tender grace of a day that is dead / [Which] Will never come back to me." The speaker is mourning someone who has, apparently, died, someone who imparted a "tender grace" to his days. Though, now, he feels that his life will lack this tenderness and, instead, be characterized by "break[s]" which are painful and violent. Thus, when the speaker references the "foot of thy crags," he isn't just referring to the literal rocks, but also to the bleak harshness of his life after he has lost his loved one.

Tennyson's poem "Break, Break, Break" is the narrator's lament for someone "vanish'd" (line 11). The image is of someone at the shore watching the waves break, feeling lonely and sad. We are given a clue in the beginning that the waves are breaking against a cliff when the narrator refers to "cold gray stones" (line 2), but this is made completely clear when the narrator refers to the "crags" (line 14). A crag is a cliff. The waves are breaking against the bottom of the cliff. When we refer to the bottom of a cliff, we often call it the foot of the cliff. This is used so frequently that most people don't stop to think of this as personification. A cliff has no feet! We use this in other ways, too, for example, the foot of the bed. The expression simply means the bottom of the cliffs.