Only the Skills in the Leadership section have the possibility of affecting pilots in a fleet. There are three types of leadership skills, those that increase your personal ability to command a number of people, those that give bonuses when you are a booster, and those that increase the effectiveness of Warfare Link modules. For any of these skills to matter, the fleet must be set up properly or else the 'flow' of bonuses will be impeded.
Command Skills:
Fleet Command: As a fleet commander, this skill allows you to pass on bonuses to wing commanders below you, to a maximum of one wing per level of the skill (5 in total). This skill requires Wing Command trained to 5.
Wing Command: As a wing commander, this skill allows you to pass on bonuses to squad commanders below you, to a maximum of one squad per level of the skill (5 in total). This skill requires Leadership trained to 5.
Leadership: As a squad commander, this skill allows you to pass on bonuses to squad members below you, to a maximum of two members per level of the skill (10 in total).
Direct Skills:
Leadership: Grants a 2% bonus to fleet members' targeting speed per skill level.
Armored Warfare: Grants a 2% bonus to fleet members' armor hit points per skill level.
Information Warfare: Grants a 2% bonus to fleet members' targeting range per skill level.
Siege Warfare: Grants a 2% bonus to fleet members' shield capacity per skill level.
Skirmish Warfare: Grants a 2% bonus to fleet members' agility per skill level.
Mining Foreman: Grants a 2% bonus to fleet members' mining yield per level.
Warfare Links are high slot modules that can only be fitted to certain classes of ships ( Battlecruisers, Command Ships, T3s with the right subsystem, carriers and titans and the indy ships ).
Armored Warfare Specialist
Allows the use of armored warfare links and increases the effectiveness these modules.
Armored Warfare Link - Damage Control - reduces the capacitor need of armor repairers and remote armor repairers by 2% per level.
Armored Warfare Link - Passive Defense - increases the fleet's armor resistances by 2% per level. This is a very useful module for armor fleets.
Armored Warfare Link - Rapid Repair - increases the speed (i.e. reduces the duration) of armor repairers and remote armor repairers by 2% per level.
Information Warfare Specialist
Allows the use of information warfare links and increases the effectiveness these modules.
Information Warfare Link - Electronic Superiority - increases the strength of electronic warfare modules. For each level, increases ECM jam strength by 2%, sensor dampener targeting range and scan resolution penalty by 1.2%, tracking disruptor optimal and falloff penalty by 1.2%, and target painter signature bonus by 2%.
Information Warfare Link - Recon Operation - increases the optimal range of electronic warfare modules by 2% per level.
Information Warfare Link - Sensor Integrity - increases the sensor strengths of all ships in the fleet by 3% per level.
Mining Director
Allows the use of mining foreman links and increases the effectiveness these modules.
Mining Foreman Link - Harvester Capacitor Efficiency - reduces the capacitor need of mining lasers and gas & ice harvesters by 2% per level.
Mining Foreman Link - Laser Optimization - reduces the duration of mining lasers and gas & ice harvesters by 2% per level.
Mining Foreman Link - Mining Laser Field Enhancement - increases the optimal range of mining lasers and gas & ice harvesters by 4.5% per level.
Siege Warfare Specialist
Allows the use of siege warfare links and increases the effectiveness these modules.
Siege Warfare Link - Active Shielding - increases the speed (i.e. reduces the duration) of shield boosters and shield transporters by 2% per level.
Siege Warfare Link - Shield Efficiency - reduces the capacitor need of shield boosters and shield transporters by 2% per level.
Siege Warfare Link - Shield Harmonizing - increases the fleet's shield resistances by 2% per level. As for its armor counterpart, this is a very useful module for shield fleets.
Skirmish Warfare Specialist
Allows the use of skirmish warfare links and increases the effectiveness these modules.
Skirmish Warfare Link - Evasive Maneuvers - reduces the signature radius of the fleet's ships by 2% per level.
Skirmish Warfare Link - Interdiction Maneuvers - increases the optimal range of propulsion jamming modules by 3% per level.
Skirmish Warfare Link - Rapid Deployment - increases the speed of afterburner and microwarpdrive modules by 2% per level.
As usual, my information is directly from the Uniwiki articles on Fleet Leadership and Warfare Links.