Can you explain this in laymen terms?

[Tamara W]

In the case of a resignation from office, unless the bylaws provide otherwise, the assembly cannot proceed to fill the vacancy immediately since notice is a requirement. But if a member is elected and declines, no notice is required to complete the election immediately or at the next meeting (see 46:46).

[Gary Novosielski]

It's drawing a distinction between a resignation of someone who is in an office, and someone who was elected, but declined the office before ever being in it.

In the former case, the vacancy can't be filled immediately, because holding an election requires previous notice, usually at least several days notice.

In the latter case, where an election is already in progress, but someone declines an office, this is not the same as a resignation.  In this case no special notice is required, you just keep going and complete the election.