I've read that the 'exposure delay mode' is useful for avoiding blurred close-up shots. Why is this and how does it work?
All recent Nikon DSLRs feature an 'exposure delay mode', apart from the most basic models like the D3400. This delays the opening of the shutter, typically by a couple of seconds, after the reflex mirror flips up prior to taking a shot. The length of delay is usually adjustable in up-market Nikon DSLRs. This pause gives the camera a chance to settle, after the jolt and subsequent vibrations caused by the reflex mirror flipping up. It's particularly useful when shooting extreme close-ups with macro lenses, and for long telephoto shots, because both scenarios are particularly prone to blurring from 'mirror-bounce'.
Exposure delay mode is usually only used when the camera is mounted on a tripod, as mirror-bounce is actually exaggerated when you're not holding the camera in a fleshy pair of hands that help to absorb the shock of the reflex mirror action.