Q:

How does this phrase illustrate the difficulty of translation

How does the aliens’ statement

“There is no time.  Many become one,”

illustrate the difficulties of translation that Louise is dealing with?  What do the world’s governments seem to think it means and what do the aliens really seem to be saying?

A:

How does the aliens’ statement illustrate the difficulties of translation that Louise is dealing with?

"Many become one" can mean many things. Maybe it means "we unite", maybe it means "only one survivor". There's a lot of interpretation here.
Similarly, the movie addresses that translations are subjective, e.g. "tool" vs "weapon". If a carpenter's hammer is a tool, it stands to reason that a soldier's rifle is also a tool. Therefore, when they show the aliens a rifle (let's assume it is being held by a soldier since there were soldiers onsite who carried rifles) and ask what the aliens' word for is, let's say they respond "flookdork".
What does "flookdork" mean? Weapon? Tool? Assault rifle? Black object? Metal object? Whatsit? You can never truly know exactly what they mean until you are able to fully speak their language (as opposed to only having a partial dictionary.
As a real world example, "schat" means "treasure" in Dutch. So I'm talking about "mijn schat begraven", i.e. how I bury my treasure. I'm telling a pirate story!
Actually, the other meaning of "schat" is a nickname for someone who you love. So when I say "mijn schat begraven", I'm talking about burying a loved one.
Before you know all the meanings of the word, you were liable to respond the wrong way. Because you assumed that your partial knowledge was the only possible answer, when in reality there was a very different meaning.

What do the world’s governments seem to think it means?

In absence of an unambiguous translation, everyone reads into it what they want to believe. 

Those who are afraid that the aliens are hostile are liable to infer malicious intent ("Many become one? They clearly want to kill us! That's a threat!").
Those who are hoping to connect with another species are liable to infer xenophilic intent ("Many become one? They want to be our allies!")

And so on...

What do the aliens really seem to be saying?

The movie intentionally only gives us the point of view of the humans. We are guessing at the meaning just as much as the characters in the movie are.
If we knew what the aliens meant, then we would respond to the humans' reaction by going "These people are wrong, these people are right" and that's where it would end. But because we do not know what it means, we cannot judge anyone's response to be correct or not.
Arrival mostly deals with how humans should interact with the unknown, before it is known. And to help paint that picture, the actual meaning of the aliens' language is withheld.

