Watch the following and you can see some of those King-threatening situations...
"Check". The King is directly threatened. [Timeline, 0:15],
Black attempts to move to get away from the advancing Queen. Unfortunately, this leaves extra space for White's Queen, who advances to the back row and is now Checking Black's King.
Another piece Blocks to protect the King . [Timeline, 0:25],
One of the options available, in this scenario, is for Black to use his Bishop to block the direct threat, by stepping in-between his King and White's Queen.
White's King escapes Check by making the capture himself. [Timeline, 0:35],
Okay, you wouldn't see Black's Queen make this unprotected move, but it gets us quickly to the point, where White's King is within legal range of movement to be able to personally deal with the threat by capturing the Queen.
King rescued by another piece. [Timeline, 0:52],
The next scenario shows the Black's King escaping the threat, courtesy of one of his other pieces ... in fact, Black has a choice - he can quash the threat either by capturing the Queen with his Knight, or with his Rook.
Check by Knight [Timeline, 1:10],
This scenario shows how the Knight doesn't have direct line of sight, but he doesn't need it because his pattern of movement allow him to jump over other pieces to capture or threaten ...
Here, the King isn't close enough to be able to capture the attacking Knight - Black's only option is to move to escape the threat.
Checked By Two [Timeline, 1:31],
This scenario shows White's Pawn capturing Black's Bishop, to land on Black's back-row, which allows him to promote his Pawn - in this case for another Queen, which directly Checks Black's King ...
But, that isn't the only threat - when the Pawn moved, it uncovered an additional threat from White's Rook, which ALSO Checked Black's King as soon as White's Pawn had finished being exchanged for the Queen.
King escapes being Double Checked [Timeline, 1:44],
Following the dual threat, in this scenario, Black's only option is to move his King, to get him to safety.
More often than not, when a King is being Checked by two pieces at the same time, it's usually Game Over - that's "Checkmate" (to be explained in another article).