Igramo društvenu igru.

Because igramo is the 1st person plural present tense form of igrati (to play).

In Serbian, the present tense can often cover both:

• we play (habitually / generally)
• we are playing (right now)

So Igramo društvenu igru. can mean either one, depending on context.

Serbian usually drops subject pronouns when they are not needed for emphasis, because the verb ending already shows who the subject is.

Here, -mo in igramo clearly means we.

So:

• Igramo društvenu igru. = We are playing a board game.
• Mi igramo društvenu igru. also means We are playing a board game, but mi adds emphasis, like we in we are the ones playing.

Because this phrase is the direct object of the verb, so it must be in the accusative case.

The dictionary form is:

• društvena igra = board game / social game

In the accusative singular feminine, it becomes:

• društvenu igru

Both the adjective and the noun change:

• društvena → društvenu
• igra → igru

So:

• društvena igra = nominative, the basic form
• društvenu igru = accusative, used after igramo

Društvena igra literally means something like social game, but in normal usage it commonly means board game or tabletop game.

So in this sentence, it is best understood as:

• a board game
• a party/game played together with others, depending on context

It does not mean a game about society. It refers to a game people play together.

No, Serbian word order is fairly flexible because cases show grammatical roles.

The neutral order here is:

• Igramo društvenu igru.

But you could also say:

• Društvenu igru igramo. — puts more emphasis on the game
• Mi igramo društvenu igru. — emphasizes we

Even though word order can change, the most natural basic version is the original one.

Serbian has no articles like English a/an/the.

So društvenu igru by itself can mean:

• a board game
• the board game

Context tells you which one is meant.

In many learning translations, this sentence is given as We are playing a board game, because that is the most neutral English version.

The base forms are:

• igrati = to play
• društven / in dictionary-style adjective form društvena = social
• igra = game

In the sentence:

• igramo is a conjugated verb form
• društvenu igru is the accusative singular form of društvena igra

So the full basic phrase behind it is:

• društvena igra

In Serbian, adjectives usually come before the noun they describe, just like in English.

So:

• društvena igra = board game / social game

And when the phrase changes case, both words change, but the adjective still stays before the noun:

• društvenu igru

That is the normal order.

Igrati is imperfective.

That matters because imperfective verbs are used for:

• ongoing actions
• repeated actions
• general activities

So Igramo društvenu igru. naturally fits meanings like:

• We are playing a board game.
• We play board games.

A perfective verb would not normally be used the same way here for a simple ongoing activity.

Yes. Igramo by itself can mean:

• We’re playing
• We play

But adding društvenu igru tells you what you are playing.

Compare:

• Igramo. = We’re playing.
• Igramo društvenu igru. = We’re playing a board game.

So the object is not always required, but it adds useful information.

For negation, add ne before the verb:

• Ne igramo društvenu igru. = We are not playing a board game.

To make a yes/no question, one common option is:

• Igramo li društvenu igru? = Are we playing a board game?

In speech, intonation can also help show that something is a question.