Diff bush or bushes are the rubber mounts that hold the vehicle differential in place.
Today it was a Mazda Tribute that received a new set of bushes. These diff bushes are subject to a lot of force from the power of the engine trying to twist the drive line. It is quite normal to need to replace these bushes in cars that are 10 yrs or more old. Not to say they cut be worn out sooner. Generally I find the rubber gives a lot of warning before they completely fail. During the vehicle’s normal services these rubber bushes are to be inspected. As they age and wear signs start with very small cracks appearing. These cracks will eventually turn into a full split, Your mechanic should advise you of this wear before it gets to the completely failed stage.
As the diff bush wears it allows for excessive movement, this movement put extra load onto other drive line components. Like the tail shaft uni joints and CV shafts.
This Mazda tribute is quite an easy replacement as the 3 diff bushes come in brackets that can be easily installed. This is no the case for all vehicles, some require a lot of labour and special tooling.