الناس يعيشون في هذا العالم.

الناس is the normal Arabic word for people or human beings in general. Even though it is a single word, its meaning is collective, so in English it is usually translated as people, not person.

A learner may expect a direct plural of إنسان (human/person), but Arabic often uses الناس as the everyday general word for people.

Because الناس refers to more than one person, the verb is plural: يعيشون = they live.

The ending -ون is the usual marker for the masculine plural in the present tense.

So:

• يعيش = he lives
• يعيشان = they two live
• يعيشون = they live (masculine plural, or mixed groups)

In Arabic, a mixed group of people is normally treated as masculine plural.

يعيشون is the indicative form of the present tense, which is the normal form when nothing changes it.

The final -ن stays because there is no particle here forcing the verb into the subjunctive or jussive.

Compare:

• الناس يعيشون = People live
• لن يعيشوا = They will not live
  Here لن changes the verb, so the final ن drops.

So in your sentence, يعيشون is simply the regular present-tense form.

Arabic allows both noun-first and verb-first word order.

This sentence is:

• الناس يعيشون في هذا العالم

That is a subject-first structure, similar to English:
People live in this world.

You could also say:

• يعيش الناس في هذا العالم

This is more verb-first, which is also very natural in Arabic.

A useful grammar point:

• When the subject comes first, the verb usually shows full agreement with it, so here we get يعيشون.
• When the verb comes first, Arabic often uses a singular verb before a plural subject, so يعيش الناس is normal.

Both are correct, but the structure changes.

الـ is the Arabic definite article, meaning the.

So:

• الناس = the people / people in a general sense
• العالم = the world

In Arabic, الناس often refers to people in general, and in English we usually just translate it as people, not necessarily the people.

So the sentence sounds natural as:

• People live in this world

not necessarily:

• The people live in this world

في is a preposition meaning in.

So:

• في هذا العالم = in this world

Like English in, it introduces a place or setting.

Other examples:

• في البيت = in the house
• في المدينة = in the city

Because العالم is a masculine singular noun, so it takes the masculine singular demonstrative هذا.

• هذا = this (masculine singular)
• هذه = this (feminine singular)

So:

• هذا العالم = this world
• هذه المدينة = this city

The demonstrative must agree with the noun in gender and number.

In Arabic, demonstratives like هذا usually come before the noun.

So Arabic says:

• هذا العالم literally: this the-world

But in natural English, we say:

• this world

Also notice that the noun is usually definite after هذا, so هذا العالم is the normal pattern for this world.

In fully vocalized Arabic, the sentence would typically be:

النَّاسُ يَعِيشُونَ فِي هَذَا الْعَالَمِ

Here is why:

• النَّاسُ ends in -u because it is the subject.
• يعيشونَ keeps its normal present-tense plural ending.
• في is a preposition.
• العالَمِ ends in -i because nouns after a preposition are in the genitive case.
• هذا is a fixed form here and does not change like a regular noun.

In ordinary writing, these short vowels are usually omitted.

In meaning, الناس refers to people in general, including men and women. Grammatically, when Arabic uses agreement with الناس, it often uses masculine plural, especially when talking about people as a group in a general way, as in:

• الناس يعيشون

That is why the verb is يعيشون.

So it is best to think of الناس as a collective word meaning people, which often takes plural agreement.

Yes, depending on context, the Arabic present tense can cover both:

• People live in this world
• People are living in this world

In many simple general statements like this one, English usually prefers live, so that is the most natural translation here.

Arabic present tense often overlaps with both the English simple present and present progressive.

Arabic usually does not use a separate present-tense verb meaning to be in simple present sentences.

So where English may say:

• People are in this world
• People are living in this world

Arabic often just uses the noun or verb directly, without a separate word for are.

Here, يعيشون already means they live / they are living, so no extra are is needed.

Yes.

• في العالم = in the world
• في هذا العالم = in this world

Adding هذا makes the phrase more specific or more immediate: this world rather than just the world.

So both are grammatical, but they mean slightly different things.