For the scientific types

Prednisone suppresses your body's immune response. Since inflammatory diseases are in part caused by your own body's immune system, suppressing it slows or stops the inflammatory process. Once the inflammation is reduced, your bowel function should return to normal. As you taper pred, the immune response returns and thus the inflammatory process returns.

People who are taking pred need to know that they need to take another medication that will treat the IBD by some means other than what pred is doing. The idea is to quickly reduce inflammation with pred and also bring along another treatment modality so that when the pred is removed the other med will continue doing its thing, whatever that is.

What is not known is why the immune system is causing inflammation in the first place. Mesalamines are essentially a topical medicine for the bowel and seem to prevent inflammation of the very first layer of bowel tissue. So if pred can reduce inflammation everywhere in the body (because it is systemic), mesalamines only affect the lining of the bowel.

As Gary said, no one really knows for sure (though characterizing such differences could have huge implications for treatment) but if I had to take a stab at explaining it, it would be one word: homeostasis. The soul purpose of the body, and indeed the immune system, is to maintain homeostasis. If we alter some bodily state (glucose levels for example) the body has mechanisms to bring it back to a normal state. By introducing a disturbance into the body (activating the glucocoritcoid receptors in this case) we are altering the normal bodily state, and so the body will do everything it can to counteract this change and return the body to "normal". Presumably, some peoples bodies are able to counteract these imposed changes, and thus, will not respond to pred as well.

This is analogous to the theorized mechanisms for TNF-alpha therapy failure that occurs over time. Eventually, the body will use other inflammatory cytokines to have the same effect TNF-alpha did and thus the inflammatory response returns. I wouldnt be surprised if that is how things worked in pred-insensitive people.

It is a little complex...

Glucocorticoids (prednisone etc) cause the neutrophils (which are the major component of white blood cells) to circulate freely, preventing attachment to any tissue.
(The prednisone binds to glucocorticoid receptors preventing attachment of white cells.)

The neutrophils (white cells) are released from the lining of blood vessels, and from any sites at which they have gathered (a process called demargination) and enter into general circulation.
Those circulating white cells are made unable to adhere, and so do not promote any further responses. This also means that the white blood cell count actually increases.

As long as the dose of prednisone is high enough, the white cells won't be able to attach anywhere, and will continue to circulate harmlessly.
As soon as the dose is lowered, the white cells are once again able to cause an inflammatory response by migrating and adhering to tissues.

Each person has a different set of circumstances regarding their inflammation.
Some need higher doses to prevent any white cells attaching to their tissues. Some have fewer sites of damage and only need a minimal dose to keep the inflammatory process at bay.

Prednisone is used in order to give inflamed tissue a chance to heal.
Unfortunately, in IBD something keeps triggering the inflammatory response, and that means the process often resumes as soon as the prednisone level goes below a certain threshold (which is why prednisone is generally used in short bursts only.)