Throughout the character's adventures, the narrator will often encapsulate a portion of the story as an encounter. An encounter is any part of the ongoing adventure whose start and end feel well defined and the contents of which are substantial towards the effort of moving the story along.
An encounter might represent "a chapter in a book" - for example, the characters show up to the castle, they are granted an audience with the king, and after a heated debate, they gain the information they were seeking, and are escorted out. The entire experience from arriving at the castle, to being forcibly removed could be considered one encounter. As another example, the characters, hot on the trails of a villain, give chase down a dark alley - they corner him and his last lieutenant, and a fight to the death breaks out; the characters are successful - this fight, on its own, might constitute an encounter.
Encounters can blend both calm situations and dire situations, for example, a royal feast that starts with good conversation and roleplaying, but breaks into a fight when an enemy queen invades in the middle of the second course!
Ultimately, it is up to the narrator as to when and where an encounter begins and ends; further, not all play time needs to be in an encounter - if the characters wish to take some leisurely time to visit various merchants, haggling for wares or brewing alchemic recipes, these activities likely do not constitute an encounter as they don't explicitly move the story along.
The purpose of defining an encounter is to award story points and optionally virtues and reputation to the player characters for the deeds they performed. At the end of an encounter, the narrator will decide how many story points each player receives, which virtue (if any) each character demonstrated, and how to modify each character's reputation in the region. The amount of SP awarded will vary depending on the narrator's judgement of how well progressed the story was, and how large a foe was defeated (if any). More on this can be found in the Narrator section, but as a rule of thumb, consider that most average encounters will award between 3 and 5 SP (while a major victory over a campaign-long villain should award significantly more).