The difference between beau, beaux, bel, and belle is based on the gender and number of the noun they modify. They are all forms of the same adjective, meaning “beautiful” or “handsome” in English.
Beau is the masculine singular form. It is used with nouns that are masculine and singular, such as un beau garçon (a handsome boy) or un beau livre (a beautiful book).
Beaux is the masculine plural form. It is used with nouns that are masculine and plural, such as des beaux garçons (some handsome boys) or des beaux livres (some beautiful books).
Bel is a special form of beau that is used before a masculine singular noun that starts with a vowel or a silent h. This is to avoid the hiatus between two vowels. For example, un bel arbre (a beautiful tree) or un bel homme (a handsome man).
Belle is the feminine singular form. It is used with nouns that are feminine and singular, such as une belle fille (a beautiful girl) or une belle fleur (a beautiful flower).
Belles is the feminine plural form. It is used with nouns that are feminine and plural, such as des belles filles (some beautiful girls) or des belles fleurs (some beautiful flowers).