Origins
The word 'crescent' preserves an ancient observation: the moon grows. It descends from Latin 'crēscēns,' the present participle of 'crēscere' (to grow, to increase), through Old French 'creissant.' When English speakers in the fourteenth century adopted the word, they were naming the moon's shape by its action — the crescent is the phase in which the moon is growing from new to full.
The Latin verb 'crēscere' traces back to Proto-Indo-European *ḱerh₃-, meaning 'to grow.' This root branched widely through the Indo-European family. In Latin it produced not only 'crēscere' but also 'creāre' (to bring forth, to create — originally 'to make grow'), 'Cerēs' (the goddess of grain and agricultural growth, from whom we get 'cereal'), and 'prōcrēāre' (to generate, to procreate). In Greek, the same root appears in 'koûros' (boy, growing youth). Through Germanic, it may be related to Old Norse 'Hroðr' and similar growth-related terms.
The family of English words from 'crēscere' is large and sometimes surprising. 'Increase' is 'in-' (into, upon) + 'crēscere' — to grow into greater size. 'Decrease' is 'dē-' (down from) + 'crēscere.' 'Crescendo' is the Italian gerund of 'crescere,' meaning 'growing' — a musical passage that grows louder. 'Concrete' comes from 'concrēscere' (to grow together) — the Romans noticed that their mixture of volcanic ash, lime, and aggregate solidified by its components growing into one mass. 'Accrue' comes through Old French from Latin 'accrēscere' (to grow toward). 'Recruit' derives from French 'recruter,' from obsolete 'recrue' (new growth, fresh levy), from 'recroître' (to grow again), from Latin 'recrēscere.'
French Influence
The most delicious descendant is 'croissant,' the French crescent-shaped pastry. 'Croissant' is simply the modern French form of the same Old French present participle 'creissant' that gave English 'crescent.' The pastry is named for its shape — a crescent moon of laminated dough. The popular legend that croissants were invented in Vienna in 1683 to celebrate the defeat of the Ottoman Turks (whose symbol was the crescent moon) is almost certainly apocryphal, but it has attached itself to the word with tenacious charm.
The crescent as a symbol has a history far older than its Ottoman association. Crescent-shaped symbols appear in Mesopotamian art from the third millennium BCE, often representing the moon god Sin (Nanna). The crescent was used by the Byzantine city of Byzantium (later Constantinople) centuries before the Ottoman conquest. When the Ottomans took Constantinople in 1453, they adopted the city's existing crescent symbol, which then became identified with Islam more broadly. Today the Red Crescent serves as the counterpart to the Red Cross in many Muslim-majority countries.
In urban geography, 'crescent' has a specific meaning: a curved street or row of houses arranged in an arc. The Royal Crescent in Bath, designed by John Wood the Younger and completed in 1774, is one of the finest examples of Georgian architecture in Britain. The use of 'crescent' for curved streets became common in British town planning and spread to cities throughout the English-speaking world.