The continuation of that quote, in reference to the line about heaven's vault cracking, speaks most to this question. Lear believes in divine justice, he believes - for example - that if he is king, he deserves by heaven to be king. And if his daughter is good, truthful, honest, then she deserves by heaven to have lived. Lear can not reconcile the idea that heaven has allowed her to die, and turns to animalistic fear and expression ("howle!") to demonstrate this latest blow to his rational understanding of the world.
The frightening message of King Learis the reason behind Lear's "howl." He learns that we can't count on divine or human justice to intervene in the worst moments of life. It is this theme that, according to the great critic Frank Kermode, makes Lear Shakespeare's "cruelest play." The play begins developing that theme in Act I with the repetition of "nothing," and the symbol of clothes (or the lack of them) develops it further, as in 3.4 when Lear says "through tatter'ed clothes small vices do appear. Robes and furr'ed gowns hide all." And under the furred gown is the naked body: "poor, bare, forked animal." It is that animal that howls in the passage you quote.