Translation:The people are glad.
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행복하다 - be happy, be contented/satisfied with the situation one is in.
기뻐하다/기쁘다 - be glad; be cheerful, joyful; feel a momentary happiness usually created by some specific event.
Like in English, 행복하다 expresses a more profound and longlasting emotional state than 기뻐하다/기쁘다. 행복하다 also gives the lasting sense of wellbeing.
In speech, 행복하다 can replace 기뻐하다/기쁘다 but it does not always work the other way around.
These are called psych adjectives and psych verbs.
A psych adjective is used to describe the (static) states, emotional or psychological, of the subject. e.g. be sad, be ashamed of etc.
When '-아/어하다' is added to these adjectives, it creates psych verbs.
A psych verb is used to express an active state of/action created by the emotion concerned.
기쁘다 (psych adjective) = be glad / contented / cheerful
기뻐하다 (psych verb) = to rejoice
사람들이 기쁩니다. = The people are joyful (static state)
사람들이 기쁩합니다. = The people are rejoicing (active state/action)
Same difference as "every•one" and "everyone" in English.
사람 = person or persons
The use of -들 is to acknowledge plurality of the subject, but it also focuses on 'individuality'. 사람들 means each and every individual member of the group "people", i.e.
사람들 = every•one(2 words); every person
사람들-이 => '-이' marker is used to introduce/set up "사람들" as topic for discussion.
사람들이 기쁩니다 [= Lit. Of being contented, every•one is.] = Every one is contented.
'-은' is used for reference (to a known/established topic) and for generalization.
사람은 = People, i.e. "all the people" or "everyone (one word)"
사람은 기쁩니다 = [Lit. About people, they are happy.] = People are contented / Everyone is contented.