Declaration of victory
A declaration (of victory) is an underplay that removes the most likely do-or-die effort when one is well ahead. It may lose points compared with ordinary maximal play, but it can be a good practical choice for winning a won game.
This is the first game Gu Li and Lee Sedol ever played. Black (Gu) has taken advantage of a ko in the upper left to create supreme thickness and is way ahead. The common move now would be to attack White's lone stone at the bottom with a but Gu chose to use his thickness to create territory with . Surely, White's centre is a bit weaker now but playing so close to thickness is a professional's way to indicate the game is over.
Interestingly, White (Lee) did not resign but lost with 5,5 points. I (Dieter) would be interested to see a professional review.
Example of a backlash
This is game 6 from the 1992 Honinbo match between Kobayashi Koichi and Cho Chikun. Kobayashi holds the White stones, and it is his turn.
According to the commentary in Tournament Go 1992, White has a very small lead. Here, White should, then, continue playing hard to convert his lead into victory. However, Kobayashi did the opposite. On his next move (62) and four moves later (66) he made underplays that, although intended to remove any comeback-chances, actually handed the initiative over to Cho, who was then able to win.
and are the culprits. They might be called a declaration in the sense that White has decided to sit on his lead rather than continue fighting. And yet this was the point Cho started to come back into the game.
At the amateur level, a declaration would be similar in principle, but more crude in its manner: it would be a big, but slack move, that hints the player thinks he or she has already done enough to win, and can now win simply by sitting back and defending, come what may.
And, to paraphrase a legend, here is what White could have won...
Here, White should have descended to . Now, Black can turn at , which is very large, but this is still outweighed by the thinness of the top left. In other words, what was played was purely defensive, declaring that "what I have is enough", but this would have continued fighting positively, seeking ways to get more instead of trying to sit back.
Also see A brilliant waste of a move.