This is a quote by Boris Spassky:
A man who is willing to commit suicide has the initiative.
Is this something that is just related to chess or is it a wider statement about people?
The context of the quote is the 1972 World Chess Championship match between Boris Spassky and his challenger Bobby Fischer. The match had a rocky start, since Fischer initially didn't show up and thereby delayed the start of the match (see Fischer Apologizes to Spassky; Plans for Match Still Unsettled in The New York Times, 6 July 1972). In fact, there was uncertainty about whether the match would take place at all; Fischer wanted more prize money.
The blog The 48 Laws of Power (an unexpected source), gives some more context to the quote (my emphasis):
Spassky tried to be patient. His Russian bosses felt that Fischer was humiliating him and told him to walk away, but Spassky wanted this match. He knew he could destroy Fischer, and nothing was going to spoil the greatest victory of his career. “So it seems that all our work may come to nothing,” Spassky told a comrade. “But what can we do? It is Bobby’s move. If he comes, we play. If he does not come, we do not play. A man who is willing to commit suicide has the initiative.”
From Spassky's point of view, Fischer was the person on the suicide mission. The initiative is an important concept in chess. Apparently, Wilhelm Steinitz said, "Only the player with the initiative has the right to attack". But it may be better to use the word "opportunity" than "right", since it means that you have the opportunity to attack because you are not in a position where you need to make defensive moves. You don't need to wait for what is going to happen; you make things happen. This is also applies to the situation that Fischer put Spassky in: Spassky had to wait for what Fischer was going to do next, there was no way to predict his actions.
The wider application of this is that someone who is on a suicide mission (either in a literal or a figurative sense) will not be constrained by the great personal costs that their actions may require, so it is harder to prepare for what they will do. This puts you in a defensive position where you need to wait for what will happen; the other person has the initiative.
The context for this quote can be found in the book The 48 Laws of Power by Robert Greene. It comes from the famous Fischer-Spassky match in Reykjavik in 1972:
In May of 1972, chess champion Boris Spassky anxiously awaited his rival Bobby Fischer in Reykjavik, Iceland. The two men had been scheduled to meet for the World Championship of Chess, but Fischer had not arrived on time and the match was on hold. Fischer had problems with the size of the prize money, problems with the way the money was to be distributed, problems with the logistics of holding the match in Iceland. He might back out at any moment.
Spassky tried to be patient. His Russian bosses felt that Fischer was humiliating him and told him to walk away, but Spassky wanted this match. He knew he could destroy Fischer, and nothing was going to spoil the greatest victory of his career. “So it seems that all our work may come to nothing,” Spassky told a comrade. “But what can we do? It is Bobby’s move. If he comes, we play. If he does not come; we do not play. A man who is willing to commit suicide has the initiative.”
-- source (emphasis mine)
In its immediate context, this is a statement about Fischer's apparent willingness to forfeit the entire tournament for the sake of details. It would be "suicide" for his chess career to walk away from this match - and yet, by holding that possibility in the air, he kept everyone else waiting for him, keeping the "initiative" in a sense.
In the wider context, this ties into Fischer's strategy throughout the tournament. You can read about this in the 2 pages following the above passage in Greene's book. He outplayed Spassky with masterful psychological warfare: bluffing, playing unpredictably, changing his strategy, and always keeping the Russian off-balance. He forfeited two games at the start, which should have made Spassky more confident but instead made him nervous because he had no idea what Fischer was doing. His complaints were part of this overall strategy: by threatening to back out, he seemed to be jeopardising his own chess career, but in fact it was a way of psyching out his opponent, as well as keeping the "initiative": it was his choice whether or not the game would be played at all.
Naturally, as a world-class chess player, Spassky would have been well-versed in matters of strategy. It's certainly possible to interpret his quote as a general aphorism about people. From a chess point of view, Fischer's actions were akin to a gambit: he took huge risks, and sacrificed two games at the start, for the price of an eventual glorious victory.