This verse describes an act of psychological warfare employed by the Assyrian army against the people of Jerusalem during King Hezekiah's reign. Let's break down the meaning:

"They called out with a loud voice in the Jews’ language...": The Assyrian officials (likely representatives of King Sennacherib) specifically spoke in Hebrew (or Aramaic, the common language of the Jews at the time). This was a calculated move. If they had spoken in Assyrian, the common people wouldn't have understood.
"...to the people of Jerusalem who were on the wall...": This clarifies that the message was intended for the ordinary citizens defending the city walls, not just the leaders.
"...to frighten them, and to trouble them...": This is the core of the strategy. The goal wasn't necessarily to launch an immediate attack. The Assyrians aimed to demoralize the defenders, plant seeds of doubt, and break their will to resist.
"...that they might take the city.": The desired outcome of this fearmongering was to weaken the city's resolve to the point where the inhabitants would either surrender or be easily overcome in battle. If the people were frightened and anxious, they'd be less effective as soldiers, and potentially even turn against their leaders demanding surrender.

In essence, the verse describes a propaganda tactic. The Assyrians used the common language of the Jerusalemites to spread fear and uncertainty, hoping to psychologically weaken the city's defense and make it easier to conquer.

This was a common tactic in ancient warfare. Undermining the morale and unity of the enemy could often be more effective than brute force alone.