Purely speculative!
The Federation Air Force is one of the uniformed services of the Gallentean armed forces, along with the Navy, Marines, Army and Customs. As one of the smaller branches of the Federal military, it acts as a primarily defensive force, the GFAF operating a variety of aircraft, drones, and orbital weapons and satellites designed to assist local forces in counteracting against invasion and incursion.
Unlike the Amarr Empire or Caldari State, the Gallente Federation does not possess devolved military forces that can match the proficiency and scale of major or minor Amarrian houses and/or State megacorporate paramilitaries. Though many worlds and colonies have their own security forces (officially designated 'planetary defence troops', such as that under Intaki authority), they often do not have the logistical nor financial capabilities to protect their planets from a full-scale assault by a hostile force. However, independent planetary governments are reluctant to offer mandates for official Army or Navy presence, as this often implies (to some degree) a loss of sovereignty, as well as an element of influence from the central Federal authorities (which is mostly always unwelcome).
As such, planetside protection from the Air Force is far more commonly franchised; the local defence forces are provided an enhanced level of movement and combat capabilities while remaining mostly independent. With the GFAF being confined to the skies and close orbit, except when needed, the Federation cannot be accused of stepping on local autonomy and, most importantly, pride.
The Senate has debated amongst themselves for almost an eternity whether to integrate the Air Force, as well as the Marines, into the Army and/or Navy where necessary. The supporters of this view point out that such an integration would save countless billions on the Federal budget each year, as the cost of maintaining two independent branches would be alleviated. In addition, they cite how other nations do not make the habit of operating no more than two military services under central authority, resulting in a far more streamlined and efficient fighting force. They often use the example of the Caldari Marine Expeditionary Forces, the infantry branch of the Caldari Navy, and their consequentially much more economical way of doing things, as well as how their air forces are often divisions of the individual megacorporate security outfits. The opposers of the move cite this exact reason as why they should not integrate the two branches, a matter of national pride to not outwardly admit that the Caldari have got it right for once.
Still, history has shown that the presence of the Air Force on a colonial world can make quite the difference. With being such a small, specialist branch, GFAF personnel are highly trained, and their equipment almost second-to-none. A world without Air Force presence in frontier and fringe territories is far more likely to pirate attack than worlds with. Local governments also prefer the level of security that they enjoy, without having to sacrifice autonomy. Air Force commanders often approach local political leaders to advise and consult, upon detecting a possible threat in the local sector (commonly Serpentis smuggling parties, Guristas pirates or Cartel slave raiders). The local leader(s) almost always, after some deliberation, request the commanders to call for Navy and/or Marine support to deter or eradicate the potential threat. It is often said that the smaller bodies of the Federation enjoy this level of empowerment that is provided to them; detractors state that this illusion of military autonomy is secondary to the safety of Federation citizens, citing that it would be far more sensible to just have a permanent Army or Navy presence, instead of wasting time with ‘superficial, self-important chin-wagging’.
Despite all its points of derision, especially in regards to sound strategy and tactics, the Federation Air Force remains an important cultural aspect for the Gallente, carrying all the trappings of being guardians of the people, freedom and liberty, without being seen as overbearing and potentially unwelcome, unlike the larger branches of the armed services.