Alfred Tennyson's poem "Break, Break, Break" speaks to the life of the sailor on the sea. The reference "break" refers to the waves which break on the shore or the rocks with such power that they break apart and they wear down (or erode) the things (like rocks, cliffs, and the beach) which they break on.
Many lives, of those who dedicate their lives, were lost to the sea. The poem, therefore, speaks to those who the sea has taken. The line "but O for the touch of a vanish'd hand" refers to those who have lost their battle with the sea and died.
This reference can be interpreted in a few different ways. First, those who have lost their loved ones desire to be touched by their hand again. Second, those who have lost their lives could wish to touch their loved ones again. Lastly, the poem has an elegiac tone (one of loss and remembrance). Therefore, the line could also speak to the fact that the day is dead and the speaker wishes for it to remain on forever. The speaker wants to be touched by the hand of the day.