If we're thinking of the same section, it states that a spent destiny point can alter details of a setting, such as what time it is. For example, one of your characters receives a note asking to meet in private somewhere. The player suspects a trap, and he is good at hiding and has the benefit "Night Eyes". He spends a Destiny Point for the arranged meeting time to be at night, where he will be able to see the person (or people) coming to meet him before they see him, giving him an advantage.
Another example. One of your players is being tried for a crime. He has made friends with (or a good impression on) King Robert. King Robert normally despises having to do kingly duties, and is not expected to be there, having arranged to go hunting instead. For a spent Destiny Point, he may have decided to postpone his trip to sit in on the trial as well, giving your player a partial ally in an otherwise hostile situation.
Some archers in the Night Watch are defending against a horde of wildlings charging across open land. For a Destiny Point, perhaps there are some easy to climb trees or large outcroppings of rock, granting the archers cover and height for increased shooting range.
Those are the kinds of examples I had in mind, manipulations to environment that give a small edge to the players.