Literally: scold – scold – big – laugh/smile
Alternately: Laughing Out Loud. Hearty laughter.
Notes: As usual, the second 呵 can be replaced with the doubling mark 々. 大 may also be pronounced dai, although this seems to be less common than tai.
While in contemporary Japanese dictionaries, 呵 appears in terms such as 呵責 (kashaku, “accuse”), the original meaning of the character seems to be something closer to “blow out air.” It’s unclear (to me) whether its association with laughter is derived from the above, or from the phonetic component ka. In either place, 呵 on its own – singly or in series – is almost certainly a phonetic representation of laughter (although in modern Chinese it seems to be pronounced hē rather than ka or “ha”).
This compound reportedly comes to us from a Song dynasty collection of biographies of Zen Buddhist priests, The Transmission of the Lamp (景徳傳燈録, in Japanese Keitoku dentouroku).