To that end, this post will act as a glossary I can point to for terms so that they do not have to be explained many times, and will grow as the list grows.
Fitting - The measure of CPU and Powergrid a module requires to be placed in a slot on a ship and turned online.
Online / Offline - A module that is on a ship can be online, where it is using up CPU and powergrid and applying any passive effects as well as being ready to be activated for active effects, or offline where it is still on the ship in the slot but does not use any CPU or powergrid, has no passive effects, and cannot be activated.
Active / Passive - An active module is one that has to be turned on for its effects to apply. A passive module applies its effects to a ship as long as its online.
Activated / Deactivated - Some modules can be "turned on" when they are on ship, in space, and online. Once activated, they apply their effects. Turning an activated module off is said to be "deactivating" it.
Rack - A collection of slots of a particular type is referred to as a "rack". For example, all the high slots are one rack, mid slots another, and low slots a third rack. Rigs are not referred to as a rack, they are just "slots".
Overheat - Most modules that can be activated have the option to operate at an increased efficiency or rate at the trade off of building up heat on the module itself as well as the rack it is part of. If too much heat builds up, the module will take damage. If a module takes too much damage, it will "burn out" and no longer work, i.e. be able to apply active or passive effects.
Meta Level - Every module has a property called a "meta level" which is an abstract measure of how good it is in theory. Meta Level 0 represents Tech 1 modules, Meta Level 5 represents Tech 2 modules.
Meta Modules / Named Modules - Many modules have one or more variants between its base Tech 1 version and the advanced Tech 2 version with meta levels ranging from 1 to 4. This group is often referred to meta modules because they are meta levels higher than Tech 1, or "named modules" because they have special names lime "Arbalest Heavy Missile Launcher". In the past these modules quality increased as the meta level increased to Tech 2, but their is an initiative to balance them so that they all have some advantage over tech 1 in different areas.
Faction Modules - These are modules that are provided by the loyalty point stores of factions (e.g. Amarr, Guristas, Mordu's Legion, etc) or from NPC loot drops of those factions. They are usually better than Tech 2 in some manner.
Deadspace Modules - These are modules found as loot drops in complexes and tend to be as good or better than faction modules.
Officer Modules - These modules are typically the best module variants you can get and are only dropped by special advanced Officer NPCs in null sec.
Storyline Modules - These are modules are are rewards for special missions and have variable utility. Due to rarity and questionable utility they are rarely used.
More to come...