Hypertext fiction is only a small part of the larger realm of "interactive fiction". I think interactive fiction is easier to explain - the idea is that different readers can choose a different path through the story, with the result that each has a unique reading (or playing) experience.
In the simplest case, there is one, set story, and the reader is only choosing what order they read the pieces in, perhaps skipping some pieces entirely. Another simple case, the reader may be asked to name the protagonist and/or the love interest, adding a small amount of personalization to the story.
Things get more complex if the story branches. This is a choose your own adventure or in video game terms a dialog choice. The writer asks the reader to make a choice for the main character, then depending on what was chosen the reader is presented with a different version of the next scene, or even a different version of the next part of the story.
Modern video games have moved beyond that to a more modular and score-based approach. For example, the game may have two opposed factions; if the player completes quests for faction members he gets positive reputation points for that faction and negative reputation points for the other faction. If the player kills members of a faction he gets negative reputation points with that faction and positive reputation points with the other faction. The game can use these scores to determine whether faction members should react to the player with admiration, politeness, suspicion, or hostility. That's only one layer. On top of that the player can gain relationship points with individual characters, which determine whether those characters are enemies, strangers, friends, or love interests in relation to the player. The character will say different things to the player based on what their relationship is. What characters say to the player is also affected by the player's progress at achieving global plot objectives. For example, at first characters may complain about the easiest villain. But after the player has defeated that villain, the characters should not complain about him any more, instead they should praise the player for solving that problem and move on to complaining about a slightly harder problem.
