Although molecular vibration is a quantum phenomenon, you can take a few lessons from classical physics. Let's consider a molecule with two functional groups, one at each end, separated by a lot of uninteresting junk. Most largish molecules are "floppy", in the sense that if you twang one end of it, the vibration is mostly dampened out by insulating junk, such that the other end doesn't really feel it that much. Think of putting your hand on one side of a long table and having a friend tap on the other end - whether you feel the vibration depends on the strength of the source vibration (how hard is the tapping), the frequency/energy (we know bass is transmitted better than treble), and how well the material conducts the vibrational energy. A soft wood, like pine, may transmit the vibration much worse than a hard wood like mahogany. Molecules are not so different, and most of the aliphatic chains (much less, space between molecules) are poor transmitters of vibrations. In this sense, FTIR is in most cases a method to identify functional groups rather than entire molecules. It is why, also, most functional groups show up around the same energy, because they aren't usually strongly influenced by what else is around. (Not to say they aren't influenced at all - they are - but for the purpose of baseline organic analysis, the shifts aren't very significant or enlightening outside of identifying that molecule A is a ketone or amide or whatever.) If the amount of intermediate junk is reduced, or if the intermediate junk is made more rigid (e.g., via carbon-carbon conjugation) vibrations are transmitted more efficiently, and one vibrating functional group can influence the vibration of another. Although true in principle for all nearby vibrations (even those in only a through-space relationship), eventually we can consider two structurally-linked vibrations to be strongly coupled, in the sense that you can't even consider them functionally separate, because pouring energy into one invariably effects the vibrational state of the other. This is the case of the two carbonyl groups in an anhydride. The carbonyl stretch is very strong (it involves a large change in dipole moment) and two of them in so close proximity means their vibrations are bound to also interact strongly. In a way, you consider these to be a single functional group- in fact we may define a functional group from a spectroscopic standpoint as a unit that behaves as a single vibrating entity. The two carbonyls can either be vibrating in concert, or... whatever you would call the opposite of in concert. It isn't really so different from the vibrational states of carbon dioxide, which also have a symmetric and antisymmetric stretch. When both carbonyl groups are attached to the same carbon, you simply cannot stretch one carbonyl without impacting the other one.
Acid anhydrides are a fairly special case of coordination of two linked molecular vibrations because the carbonyl stretches are so spectroscopically significant. Although in principle any one vibration will transmit some energy to other nearby vibrations, standard (steady state) FTIR approaches aren't usually sensitive enough to deconvolute these physical relationships. Using techniques like 2D FTIR, however, you can selectively feed energy into one vibration and probe how that energy is transmitted into other nearby molecular regions. This has been immensely valuable in, say, polypeptide analysis, where the cross-talk physics between nearby vibrations (time delay and magnitude of energy transmission) provides a lot of detail on protein structure.