Restructuring generally means the team is taking either the base salary or roster bonus owed to a player and turning it into a signing bonus.
The benefit for the team is they can spread signing bonuses out up to 5 years of a player's contract, thus lowering the cap hit of the player for the upcoming season. The benefit for the player is they receive a signing bonus check immediately rather than wait for the roster bonus due or have to earn the base salary
In Knox/Von's case, what they're technically saying is they reworked their contract aka took a paycut to help the team.