Somewhat simplified explanation - because of quite normal effects of radio propagation, including reflection from buildings, land masses, and various other matters, the VOR signal you receive may not have travelled in a straight line. The practical effect of this is that the apparent radials you receive in your aircraft are not perfectly straight lines back to the beacon, but might have a wobble in them. As far as possible, VOR beacons are installed in such a way as to minimise these imperfections, but they inevitably exist to some extent.
If you fly along a beacon following a VOR radial, using the CDI, keeping the needle perfectly in the middle, you may not actually be following a perfectly straight line on the ground. You will be following any slight bends in the radials. For most of the time you will never notice, because the error will be only 1 or 2 degrees, and you're unlikely to see that slight curvature. If you fly in an area promulgated as affected by significant scalloping, you might actually notice you need to keep changing heading to keep the CDI centered. In extreme cases the needle will move around faster than you can keep up with it!
If you have a multi-sensor FMS (particularly one with satnav) then it will do a better job of flying straight lines along the ground. If you set the autopilot to follow the FMS, following a track directly to a VOR, and meanwhile set the #2 CDI to line up with the VOR radial, it is quite common to then see the VOR radial wander a little to the left or right, as the aircraft bores a straight line through the sky.
Well said C J Driver, a good explanation in easily understood terms.
I would like to add 2 points addressed to kuobin's query regarding the EFFECT upon FMS / FMC equipped aircraft -
(1) It should be remembered that many SIDs, STARs, and Non-Precision approaches are based upon VORs, each of which may well have a small degree of scalloping (most do to a small degree). This is well within tolerances, and, airways surveyors have flight tested the applicable procedures based upon VOR indications, not what they should indicate in an ideal world. It is essential therefore, that when flying a SID, STAR or VOR approach using the FMS for tracking, that the VOR be simultaneously monitored for deviations within the laid down tolerances (normally 1 dot or half a dot). If VOR indications were to move outside tolerance, then reversion should be made to Radio-Nav indications. During a VOR approach, it may well be more appropriate to carry out a missed approach.
(2) If you DO have a multi-sensor FMS, VOR indications may well be a part of the position update to the Inertial position. Admittedly, VOR update comes after GPS, LLZ/DME, DME/DME in the 'pecking order' for most reliable position, but there are many instances where a single VOR/DME couple may be the only external reference for update. You should be well aware of unreliable or scalloping VORs from NOTAMs / Airways Manual etc. so these rogue VORs can be VOR inhibited on your FMS.
Scalloping also affects the GS I'm led to believe.
One can see the ICAO ILS Permitted Guidance Errors in an interesting AIAA paper here amongst other places.
Of course, whilst approaching the limits of the certified area, I've always thought the GS onto RW 14 @ AGP was a classic illustration of this. I've seen some interesting altimeter readings at various distances from the field inbound.
Errors that neither temperature corrections or altimeter errors would seem to explain.
A good twist on the original thread SR71, GS scalloping can be severe in some instances. It should be remembered that the nominal surveyed area for Localiser is 25 NM, the surveyed area for GS is the same 25 NM longitudinally, but within Localiser coverage laterally. NOTAMs / Airways Manual notification may indicate lesser tolerance at various locations, and conversely, at some locations GS is airways tested and certified at lateral limits outside the Localiser coverage.
The worst case I've seen is at Phuket (VTSP / HKT) in Thailand RWY 27, where steady 'on Glide Slope' indications are common when tracking to intercept the localiser, but suddenly jump to 'full fly up' when established on the Localiser - Users BEWARE!
On the other side of the coin, it was once common to have ATC instruction in Singapore to "Descend on the Glide, call established on the Localiser". (I haven't heard this one for some time now, perhaps they don't include this larger area of GS coverage in the regular airways testing / calibration any more).