Modules
A module in EVE Online is an item that may be fit (that is, attached) to a ship that either improves the attributes of the ship (for example, an armor plate increases the amount of armor of the ship), grants the ship some sort of functionality (for example, an autocannon allows the ship to shoot other ships), or improves the attributes of other modules on the ship (for example, a gyrostabilizer increases the damage done by projectile weapons including autocannons).
Prerequisites
In order to fit a module to a ship, you must have two things: the prerequisite skills for the module and a ship that can accept the module. (By implication, you must also have the prerequisite skills needed to fly the ship, but that is beyond the scope of this article.)
To see if you have the necessary skills to use a module, SHOW INFO on the module and click the PREREQUISITES tab. That will show you the skills needed to make use of the module; these skills are needed both to fit the module to your ship and to enjoy the benefits of the module. If the skills themselves have other skills as prerequisites, then these will also be shown on the PREREQUISITES tab of the module information.
To see if your ship can accept the module, SHOW INFO on the module and click the FITTING tab. All modules can only be fit to discrete slots on a ship. Additionally, many modules require that the ship they are fit to provide some amount of CPU (measured in teraflops or "tf") and powergrid (measured in megawatts, or "MW") to keep the module online. The sum total of the CPU and powergrid requirements of all modules that are fit to the ship and online must be less than or equal to, the amount of CPU and powergrid that the ship can provide.
Module status
A module can be unfit, fit, offline, online, inactive, and active.
"Unfit" means that the module is not in any of the slots of a ship. It has no effect on the ship (aside from taking up space in the cargohold). It won't show up on the module interface next to your capacitor.
"Fit" means that the module is in a slot on your ship. If the module has any drawbacks (that is, disadvantages), then those drawbacks are being applied to your ship. Fit modules may be offline or online.
"Offline" means that a fit module is not providing benefits, but also is not using any CPU or powergrid. Keep in mind that if a module has any drawbacks, then your ship still suffers those drawbacks even if the module is offline but fit. Depending upon your interface settings, offline modules will appear on your module interface next to your capacitor, but will be dim.
"Online" means that the module is currently fit and using some of the ships CPU and powergrid. To enjoy the benefits of passive modules, you only need the module to be online. Active modules are a bit more complicated, as explained below. Online "active modules" may be Inactive or Active.
"Inactive" means that a module is fit and online, but not providing its full benefits, performing it's full function, or using capacitor energy. Some modules will provide a limited benefit while online but inactive, other modules provide no benefit whatsoever while online but inactive; which the case is depends upon the module in question. In either case, the module is still applying any drawbacks it has and occupying CPU and powergrid. Weapons that are ready to be fired, but aren't actually shooting anything, fall into this category.
"Active" means that the module is fit, online, using capacitor energy, and providing it's full benefit or functionality. Weapons that are firing on targets fall into this category.
