Digital photography, a fairly recent invention, has had major ramifications in all aspects of photography, not least wedding photography. The term wedding photography, by the way, refers to the photographic activity that takes place before, during and right after wedding ceremonies. Such photography is considered an integral part of the wedding ceremony; very much like the white gown, the procession and the wedding cake. A modern wedding ceremony without photography would be considered incomplete, just as a modern (western-style) wedding would be considered incomplete without a cake for the groom and his bride to 'cut.'
Now one effect that digital photography has had on wedding photography is that there is no longer much panic when the hired photographer does not show up. The Y generation may not really understand this, but just a few decades ago (before the advent of the digital camera), photography was a very specialized art/science: like medicine or engineering. Only the specialists could do it. Not everyone could be a photographer. So if on a wedding day the hired photographer failed to show up, panic was sure to set in. It was not unheard of weddings even being postponed on that account only; for how could the couple say they were wedded when there was no photographic evidence for the fact?
Thanks to digital photography, everybody is now a photographer. Even many modern phones come with digital cameras. So if the hired photographer fails to show up, that is his loss. Someone will take their digital camera (or their phone), and start recording the event for posterity. No need for panic whatsoever.
Indeed, cash-constrained couples are opting not to hire a photographer for their weddings. Rather, one of the friends in attendance, who has the sense to use a digital camera well is assigned the task of clicking at the most crucial moments. Better still, two different friends are assigned the task, so that in case one doesn't get it right the other one surely will.
Talking of 'getting it right,' the second effect of digital photography on wedding photography is that it has reduced the incidences where wedding photographs got 'burned' (overexposed) or otherwise messed up. The precursor to digital photography, which was film-based photography used to be open to so many complications. In other words, so many things could go wrong. Not so with digital photography. But should something go wrong still, there is always a chance that someone else clicked away at the event in question (seeing that everyone is a photographer now), so that the damage is minimal anyway.
The third effect of digital photography on wedding photography is that it has made it less expensive. The photographer using the digital photograph really only has to care about running out of charge on his camera. Nothing else gets 'consumed' and the whole thing is extremely cheap. Now compare this with traditional photography - where there was always the cost of the film to contend with (or at least the risk of running out of film where the cost was not an issue) - and you see just how much of an improvement digital photography is.