大哥大 originally referred to the large, brick-sized portable telephones of the 1980s and 1990s — the first generation of mobile phones, also nicknamed 'the brick'. Because these phones were expensive and status symbols, the word got extended to mean a powerful, wealthy person, often a boss or godfather in organized crime or business contexts (especially in Hong Kong triad slang). The phone sense is now outdated (use 手机 instead), but the 'big boss / godfather' sense is still current in informal language.