Bit of everything - when I was a restaurant manager the specials consisted of

a) seasonal items that were only good for a short time / limited availability (say English asparagus with poached local duck eggs) that it made no sense to add to the regular menu
b) items that we had more than normal of - we would never use 'bad' food, but if we ended up with an excess of chicken that would go bad in a few days' time, then we would add a chicken special as part of stock management. We also did this when a supplier mis-delivered (they normally would tell us to keep extra delivered items, so we could well have an extra box of chicken to get through, or a box of calamari that we didn't normally serve).
c) Ideas we wanted to try out either for regular menu items, for catering etc.
d) Me playing in the kitchen - I love cooking, so once in a while (usually if we had a slow day) I would create a dish or two that would feature as specials.
e) Kitchen malfunctions - either of staff or equipment! For example, if one of the fryers was broken then we would have 'specials' that sounded delicious that only required the oven or a pan (e.g. roasted chicken served with mashed potato and braised leeks, rather than beer battered fish & chips) or if we had a shortage of staff, we'd play to our strengths (some people could cook meat far better than they could cook fish, for example, or push a less labour intensive dish, like a cassarole, that required very little chef hands on time to reduce pressure on staff).
f) Special occasion dishes - these were probably the worst option you could pick, honestly! We would cash in on a particular thing, say, St. Patrick's Day, and serve a Guiness pie, or champ, or potato soup - these items were generally lower cost to us, but with a profitable mark up (as we could only guess at how well they would sell, and because of a limited duration, they couldn't be prime ingredients). Still perfectly nice food, but in value for money terms, not your best option.