Niall's right that the vast majority of courses that have heather have it because it is native to the site. There are a few where it is been successfully planted from scratch, most notably Queenwood (whose heather was sourced from Hankley Common).
The key reason, imo, for wanting heather on courses located on appropriate sites is that it is a scarce and valuable ecosystem. If we confine ourselves to considering the lowland heath south and west of London, this is a landscape that has declined massively in the last two centuries because of the development of the region. Heath was a landscape that was created by the clearance of the original, poor quality, woodland for grazing thousands of years ago. When it is not grazed or in some other way maintained, the poor quality woodland, first birch and then pine, eventually repopulates the area. This is why so many 'heathland' courses are now more akin to poor quality woodland.
In pure golfing terms, I personally value heather primarily for its aesthetic appeal. As Niall says, it gives unmatched texture to a course, and when in bloom in late summer, nothing is so beautiful. It is unarguably very difficult to play out of, and most heathland courses have been at some time a little ambivalent about it for this reason. Fortunately (imo) the pendulum has swung back in the plant's favour of late.