Onomatopoeic — 嚎啕 (háotáo) imitates a loud, uncontrolled cry, and is paired here with 大哭 for intensification. The crying is loud and uninhibited, not quiet tears; use 默默流泪 or 啜泣 for silent weeping.
mistakes
Often miswritten as 号啕大哭 or 嚎陶大哭; 嚎啕 is the standard form in modern dictionaries. CC-CEDICT lists it as 嚎啕大哭 / hao2 tao2 da4 ku1.