Electronic Warfare refers to modules that tamper with the electronics of your own or your target's ship. There are four main categories, namely ECM with its countermeasure ECCM, Tracking Disruption with its countermeasure Tracking Computer, Sensor Dampening with Sensor Boosting being the counterpart and target painting, which doesn't have a countermeasure. Generally all races can use any kind of Electronic Warfare, though there are ships that give bonuses to certain types. Another category is the modules that pin down a ship as in either slowing it down or preventing it from warping. 

ECM
Favoured by:
some Caldari ships

Modules:
Multispectral Jammer - effective against any race but weaker than the race specific versions
Magnometric Jammer - effective against Gallente
Ladar Jammer - effective against Minmatar
Radar Jammer - effective against Amarr
Gravimetric Jammer - effective against Caldari
ECM Burst - effective against any race, but high demand of capacitor

Rigs:
Particle Dispersion Augmentors - strengthen jamming, but decreased shields as a drawback
Particle Dispersion Augmentors - increase optimal range of Electronic Warfare modules, but decreased shields as a drawback

Drones:
Hornet EC-300 (light)
Vespa EC-600 (medium)
Wasp EC-900 (heavy)

Modules used as a countermeasure:
Sensors (Multi-spectrum, Magnometric, Ladar, Radar, Gravimetric)
Sensor Backup Arrays (Multi-spectrum, Magnometric, LADAR, RADAR, Gravimetric)
Projected ECCM (used on frienuly ships but don't have any effect on the own ship)
Electronics Superiority Rigs

How it works:
ECM modules/drones disrupt the targeting abilities of the other ship for 20 seconds. This is chance based and influenced by the jamming strength of the Eve Isk module/drone and the sensor strength of the target ship.

How the countermeasure works:
ECCM and Sensor Backup Arrays both increase the sensor strength of a ship, which lowers the chance of a jam. ECCM is more effective, but uses capacitor, as opposed to Sensor Backup Arrays.
Tracking disrupting
Favoured by:
some Amarr ships

Modules used:
Tracking Disruptors

Rigs used:
Particle Dispersion Augmentors - increase optimal range of Electronic Warfare modules, but have decreased shields as a drawback.