Administration Rating: Used by Civilian Administrators and Scientists to indicate the size of colony / number of labs they may oversee at one time.
Communications: Used by Task Force Communications Officers to pass orders and coordinate the fleet. Important if you use 'Inexperienced Fleet Penalties'. Also assists in attempting to establish communications with alien races.
Diplomacy: Used my Diplomatic Team members to make other races/empires like you (or hate you less). Important if you ever want to do anything other than conquer & destroy. Also used by Task Force Public Relations officers to convince the gullible public that your ships are better than they are, and up their perceived Planetary Protection Value.
Espionage: Used by Espionage Team members to steal info from (designs, technology, survey data) and sabotage (installations) other races/empires, and to defend your empire from such activities by others.
Intelligence: Used by Task Force Intelligence Officers to discern enemy capabilities, interpret sensor data, and identify enemy classes & ships. Basically, everything found on the Ctrl F5 'Intelligence & Foreign Relations' window that isn't 'Political Relations'. Also used to interrogate captured enemy personnell.
Logistics: Used by Ship Commanders, PDC Commanders, Task Force Logistics Officers and Civilian Administrators to decrease the loading/unloading time* of their ships/PDCs/Task Force members/any military unit at their colony, or any civilian unit if the colony has a civilian spaceport.
*Of cargo, passengers, cryo tubes, Marines, ammo, fuel, and maintenance supplies - assuming Steve remembered to program it in for all those topics. Occasionally we discover he missed something, or added something new.
Operations: Used by Task Force Operations Officers to coordinate the fleet. Important if you use 'Inexperienced Fleet Penalties'. Also used in 'Task Group Training' to overcome said penalties
Survey: Also used by Geological Team members to discover additional, overlooked TNE on colony worlds and Task Force Survey Officers to grant a bonus to the Survey efforts of all ships in the Task Force in the same system as the TFSO.
Xenoarcheology: Used by Xeno Team members to investigate alien ruins, identify the builders, and designate 'recoverable' tech, installations, or components. Also used by Engineering Reg't (Brigade) commanders to recover the aforementioned items and put them into working order.
Wealth Creation: Used by Civilian Administrator to increase the 'wealth points' (Quatloos, Megabucks, Newyen, Credits, Lunies, whatever) generated by population & Financial Centres under their control.