头角 almost never appears alone — it lives inside the set phrases 初露头角 (chū lù tóujiǎo, 'first show one's horns/talent') and 崭露头角 (zhǎn lù tóujiǎo, 'distinctly show one's talent'). Learn the chunks, not the bare noun.
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Literally 'head-horns.' The image is a young animal's antlers just starting to emerge — a tidy metaphor for budding talent. Same picture as the English idiom 'lock horns,' different application.
