Hey Hoggardhigh,
The term "resonance", in this context, would mean that when the guns are fired a vibration is caused in the wing structure. Just causing vibration in the wing structure is not necessarily a problem, but in come cases the wing structure could act like a tuning fork, picking up the vibration of the guns firing and magnifying it. When this happens there may be many results, including but not limited to:
Sympathetic vibration in other areas of the aircraft, which could cause:
Discomfort.
_____Have you ever had the pleasure of driving over the road grates at the approach to a stop sign or intersection? and tried to read the instruments? or been made nauseous by a sound or combination of sounds?
Damage.
_____If the vibration is just right and just strong enough, it can cause what is generally called destructive harmonics. Destructive harmonics often occur when some of the peaks and troughs of the vibration line up, magnifying the 'beat' of the sound. Different materials and structures have different frequencies where this alignment occurs, and often multiple frequencies where this occurs. These destructive harmonics can cause/encourage several types of failure including, but not limited to:
_____Fatigue failure (cracking, shearing, and tearing) of structural members.
_____Breakage of more fragile components (the glass shell in vacuum tubes for example).
_____Self disassembly (sometimes called 'working') of components (i.e. loosening of bolts and fasteners, stretching of rivets, unseating of vacuum tubes).
_____Misalignment of components (i.e. gunsights, guns).
Non-structural failure of a system.
_____Vibration is never good for electronics and was very bad for the radio equipment of the time, causing the sets to detune. Even vibration of wire antennae could cause an increase in noise over radio channels, making it harder to understand the person talking.
_____If the vibration of the guns caused/initiated a vibration of the wing that was of the type that caused the geometry (AOA and twist) of the wing to change at the right frequency, flutter in the wing control surfaces could occur and the controls could become unmanageable. In addition, the vibration of the wing (which might not be of significant consequence itself) might cause flutter in the tail structure/control surfaces via the air flow, again becoming unmanageable. (Either of these could of course lead to structural failures and/or crashes.)
_____Or it might be simply that the vibration causes flexing of the guns which then spray bullets over a wider area.
NOTE: I may not have used the term "flutter" correctly in my explanation, as I am using it in the general engineering sense, but in popular use it seems to be referencing a rhythmic pitching or yawing motion of the airplane caused by the lack of authority of the control surfaces, and not specific as to the initiating cause??