Barnen leker på gården medan mamman står på balkongen och tittar på dem.

Swedish usually marks definiteness by adding an ending to the noun instead of putting a separate word before it.

• mamman = the mother
• gården = the yard / courtyard
• balkongen = the balcony
• barnen = the children

So the ending does the job that the does in English.

A useful extra point: if there is an adjective, Swedish often uses both a separate article and the ending, for example den stora balkongen = the big balcony.

Because barnen is the definite plural form: the children.

• ett barn = a child
• barn = children
• barnen = the children

Barn is one of those Swedish nouns where the indefinite singular and indefinite plural look the same. The definite plural adds -en.

Mamman means the mother, referring to a specific mother already understood from the context.

In Swedish, family words are often used in the definite form in storytelling or description:

• mamman = the mother
• pappan = the father
• barnen = the children

Mamma by itself is more like Mom as a name or form of address.
Deras mamma would mean their mother, which is more explicit than the Swedish sentence needs.

Swedish normally uses the plain present tense for both habitual actions and actions happening right now.

So:

• Barnen leker can mean The children play or The children are playing
• mamman står can mean the mother stands or the mother is standing
• tittar på dem can mean looks at them / is watching them

If Swedish wants to make right now especially clear, it can add words like nu or just nu.

No. Swedish verbs do not change for person or number.

For example:

• jag leker = I play / am playing
• du leker = you play / are playing
• barnen leker = the children play / are playing

And similarly:

• jag står
• hon står
• de står

The form stays the same.

Medan means while.

It connects two actions that happen at the same time:

• Barnen leker på gården
• medan mamman står på balkongen och tittar på dem

So the sentence structure is basically:

The children are playing in the yard while the mother is standing on the balcony and watching them.

A useful note: medan introduces a subordinate clause. If that clause comes first, the main clause changes word order:

• Medan mamman står på balkongen och tittar på dem, leker barnen på gården.

Swedish often prefers a position verb where English might just use be.

Here, står literally means stands, so the sentence tells you the mother is in a standing position on the balcony.

This is very common in Swedish:

• står = is standing
• sitter = is sitting
• ligger = is lying

So mamman står på balkongen is more natural and more specific than a simple mamman är på balkongen.

This is a very common Swedish pattern. It is often called pseudo-coordination.

står ... och tittar literally looks like stands and watches, but in natural English it often means something like:

• is standing there watching
• stands watching

The first verb gives the physical position, and the second gives the main action.

So here the mother is both:

• standing on the balcony
• watching the children

But Swedish packages that very naturally as står ... och tittar.

Because titta normally goes with the preposition på when it takes an object.

• titta på någon/något = look at someone/something, watch someone/something

So:

• tittar på dem = looks at them / watches them

Compare:

• ser dem = sees them
• tittar på dem = looks at them / watches them

English speakers often want to drop the preposition, but in Swedish på is required here.

Because dem is the object form, while de is the subject form.

• de = they
• dem = them

In this sentence, dem comes after the preposition på, so it must be the object form:

• tittar på dem = watches them

A useful pronunciation note: in everyday spoken Swedish, both de and dem are often pronounced dom.

Because Swedish prepositions do not always match English ones exactly.

• på gården usually means in the yard / in the courtyard
• på balkongen means on the balcony

For places and surfaces, på is very common, but the choice is often partly idiomatic. It is best to learn these as natural combinations:

• på gården
• på balkongen
• på gatan
• på landet

So even if English uses in somewhere, Swedish may use på.

Here gården most likely means the yard, the courtyard, or the outdoor area around a building.

In this sentence, the most natural picture is that the children are outside in the shared yard/courtyard, while the mother is on the balcony watching them.

It does not most likely mean the farm here, even though gård can sometimes refer to a farm in other contexts.

It can definitely be rearranged.

The original sentence starts with the main clause:

• Barnen leker på gården medan mamman står på balkongen och tittar på dem.

You can also begin with the medan clause:

• Medan mamman står på balkongen och tittar på dem, leker barnen på gården.

That is still correct Swedish. The important thing is that in the main clause, the finite verb must stay in second position, so after a fronted clause you get leker barnen, not barnen leker.