What does the military term refuse the line mean?

Answer 1

This may mean to regather the line, or making different formations of a defensive line closer to each other.

Actually, it's a specific command for larger units. It was particularly common prior to WW2, especially in the ages where men fought in larger, dense formations.

The command "refuse the line" indicates that the unit's formation should change its facing (i.e. the direction against where attacks are to be expected from, and thus, the main axis of defense) by 90 degrees. Thus, the command was usually "refuse the line RIGHT" or "refuse the line LEFT" to indicate which way the unit should turn and redeploy to defend against attack.

Refuse the Line was a command made to a unit in a stationary defensive posture, and was specifically to defend against an attacker attempting to make a flank attack against the unit. When on the march, the command would be "Wheel [Right/Left]" instead, to indicate that the unit should bear right or left sharply.