Learn Swedish: Varför bråkar barnen med varandra idag? - Why are the children arguing with each other today?

Varandra means "each other". Just like in English, it comes after the preposition med (with) to show that the children are arguing with each other. It stays exactly the same no matter who the subject is.

Does bråkar mean "arguing" or "fighting"?

It can mean both! Att bråka is a very common verb used for verbal arguments (bickering) but also for physical fighting, especially among kids. Depending on what they are doing, these children could be yelling at or wrestling with varandra.

Why does the verb bråkar come before the subject barnen?

This is the Swedish verb-second (V2) rule in action. Because the question word Varför (why) takes up the first position in the sentence, the verb bråkar must take the second position, pushing the subject barnen right after it.

Why is "the children" written as barnen? Don't plurals usually end in -ar or -er?

Barn is an ett word that doesn't end in a vowel (ett barn). These types of words look exactly the same in the plural (so "children" is just barn). To say "the" children, you add the definite plural ending -en to get barnen.