Learn Polish: W ciepłych krajach ludzie są często szczęśliwi. - In warm countries people are often happy.

The noun kraj (country) becomes krajach in the locative plural. The great thing about the locative plural is that almost all nouns, regardless of their gender, simply take the ending -ach. Since we are saying 'in countries' (w krajach), we use this case.

Why does the adjective ciepłych end in -ych here?

Ciepłych is in the locative plural to match the noun krajach. For adjectives in the locative plural, the ending is always -ych or -ich for all genders. Since the base word is ciepły (warm), we just swap the ending to -ych.

Is ludzie the plural form of człowiek (person)?

Yes! The word człowiek has a completely irregular plural. You never add a normal plural ending to it; instead, the whole word changes to ludzie (people). It is always treated as a masculine personal noun.

Why does szczęśliwi end in -i instead of the normal plural ending -e?

Because ludzie is a masculine personal noun (a group of people that could include men). Adjectives describing masculine personal nouns in the plural take special endings, which often cause a slight spelling change at the end of the word. Here, szczęśliwy (happy) changes to szczęśliwi. If you were talking about objects or a group of only women, you would use szczęśliwe.