Loosely defined world is "open world sandbox" roleplaying equivalent.
Essentially it avoids static storylines and quests/dialogue choices from influencing player experience. Alternative means of establishing non-interactive and semi-interactive atmosphere can create much greater immersion.

1.Sound/Visual realism(project a specific atmosphere for the area):
footsteps, sounds of wind/rain/snow. Positional audio(usually with compressed distances).
Interactive terrain, plants, objects(traps, levers, doors(limited in quantity),portals, ladders, treasure piles, chests and containers). Note that visual realism should be balanced with costs of displaying it, so when on low-end computers where all eyecandy is turned off the atmosphere of the game is preserved.

2.Backstory elements exposed by player character: inscriptions, scrolls found, statues/art objects, visual cues and general atmosphere created by background sounds/animations.
Game lore can appear in websites, works, art without being in game: this allows reducing efforts at making the game by making in-game lore brief and vague: effective ideas to explore is "hidden lore","alternative interpretations" and "multiple sources combine to a complete picture".
see http://videogamedesign.wikidot.com/leveldesign:backstory for hints.

3.Open-ended, loose story line: Storyline isn't told piece-by-piece by NPCs but appears as loosely connected elements that player collects from different sources(some of which may be lore or NPC stories). In general avoid forcing the player to do something(such as "if you don't do X the world is doomed") and avoid creating a concrete narrative: multiple narratives should have the same priority and different sources will provide their unique insights.
Base storyline on following disconnected backstories and lore spread through the game instead of concentrating it into a linear narrative.

4.NPC quest interaction reduced:
NPCs don't give quests(but may talk about it), quests is triggered by entering an area.
NPCs don't finish quests(but may congratulate the player), they end on the accomplishment of their objective.
NPC don't give rewards for quests, quest reward is distributed by accomplishment of an objectives of the quest or as access to area(e.g. to treasure chests).

5.No central narrative, central quest chain, central goal: avoid linear A to B progress and instead separate storyline interactions into area-specific quests, connected by lore only.
This approach scales out much better than growing extra quests and adjusting the storyline to accommodate them. Don't add concrete goals to quests that signify that A depends on B and in general loosely defined world doesn't need a "quest chain". Everything is non-linear and disconnected as much as possible from influencing each other.

6.NPC dialogue choices:
Loosely defined world would allow you to backtrack/apologize and reset NPC interaction: no permanent choices and no fixed consequences,
i.e. avoid making the choices in NPC dialogue a central piece of character development - instead alignment system(alignment points for specific actions) and wider interaction with the world will choose baseline character development and player defines the rest himself"
paths, choices, dialogues are not central components as no global linear storyline exists - everything is local, fragmented and area-specific.
NPC tips:
Avoid making the NPCs as representative of one faction or group, they're individuals with their own agenda and outlook. i.e. interaction with a NPC(GroupA) isn't considered as interaction with GroupA as a whole.
NPCs are not gamemasters: they don't have access to alter your character stats or do anything besides trading and combat(as realistic interaction).i.e. UI elements replace NPCs function related to gameplay(such as giving perks/skills or some reward/access right).
NPC are not part of storyline: storyline is about the player and player only. He chooses how to proceed in a "loosely defined world" and what changes he may bring to the world(i.e. he might help in one quest or ignore another, there is no railroading into "you must save the world" storyline).