When documents were made of paper, you needed something flat to lay them on in order to read them easily or write neatly on them. A desk is one option, but if you’re on the move, you need a mobile rigid surface, ideally one with a way to immobilize the document in question. The clipboard is a board with a spring-loaded clip attached to hold a document or stack down on it. Thus, the clipboard became synonymous with moving documents around, and making edits on the fly.
Working on a computer, a person may ask, quite reasonably: “When I ‘cut’ some text, where does it go before I ‘paste’ it?” The real answer is, of course, RAM or some such, which is not helpful. Instead, the clipboard is evoked as temporary storage for cut and copied content. While it usually is not visible as such, the symbol does appear now and then when in contexts where that content needs to be surfaced.
A secondary use of the clipboard is occasionally found in contexts like to-do lists, doctors’ notes, and other situations where, in a paper-based office or lab, a clipboard would be used to hold those things. But the connotation is largely the same.