Learn Icelandic: Barnið er að hlaupa úti. - The child is running outside.

It uses the Icelandic present continuous pattern. You take a form of vera (to be) - which is er here - and add að plus the basic infinitive verb hlaupa (to run). Together, er að hlaupa means "is running".

Does að hlaupa translate to "running" on its own?

No, að hlaupa simply means "to run". It only translates to an "-ing" action in English here because it is part of the vera að structure. Without a form of vera (to be) in front of it, it just means "to run".

Why does the sentence use barnið instead of just barn?

Barn means "child". Icelandic doesn't have a separate word for "the" that sits in front of the noun. Instead, it attaches a definite article to the end of the word. Because barn is a neuter noun, it gets the ending -ið, becoming barnið (the child).

I have seen the word út used for "outside". Why does this sentence use úti?