I am going to attempt to make myself sound intelligent and respond to this...
The way I see it, each "empire" has separate motivations because of a very different perspective on existence and subsequent purpose. For instance:
The Amarr are driven by their religion, so much so that they have formed a theocracy. (Which is actually an aristocracy ruled by an parliamentary monarchical theocracy.) Their religion teaches them to be introspective, constantly examining themselves for righteousness and then tasks them with the purpose of spreading their religion to every planet in the heavens. Several doctrines in their religion dictate what is acceptable and what isn't, hence the disdain for capsuleers (and clones in general), their viewpoint on the Matari (and subsequently every heathen) and the way they interact (or don't) with others. The greater plan for the Amarr is for all people to be under their rule, under their god until their god brings all people into his presence.
The Matari are driven primarily by two things: an intimate spiritual connection to the worlds and lives around them (Matari spirituality) and freedom of tribal identity (various cultures all beheld to the same spirits but admonishing different ones and different aspects of them). Primarily, the Matari have a "spirituality" belief, in that they understand there to be several spirits that are constantly guiding creation toward its ultimate resolution. (Some would call the spirits "gods" but to Matari see them far more intimately than that, something much more personal.) They believe that these spirits dictate destiny and purpose to each person, manifested in the Voluval and that each person's task in life is to fulfill their destiny in order to join with the spirits upon death. The ultimate goal of the Matari would be a fulfilled life leading to a peaceful death accomplished by service to family, clan and tribe in tune with their guiding spirits.
The Gallente are primarily driven by liberty and individual freedoms. As such, they tend to have no overpowering theological or religious motivation and their political position tends to be driven by whatever the most popular and influential viewpoint is at the time. Because of this, they tend to grown on all forms of oppressive expansion or enforced conformity and believe that everyone should be free to live and die as they choose. The ultimate goal of the Gallente would be absolute freedom for everyone to live their life as they see fit, subject to whatever god, spirit or belief (or lack thereof) that they choose to be and that all of humanity be humane to one another unto that end.
The Caldari are driven by a belief that their ancestors are watching over them, that family name and honor are of the utmost importance and the primary duty to each individual. As such, each person must strive to dedicate their all toward their family and subsequently humanity through their talents and merits. Those who do so will be revered, respected and elevated in society. The ultimate goal of the Caldari would be that each human would be judged according to their merit, giving all toward the advancement and betterment of humanity as a whole and thus bringing honor and respect to themselves and their family.
Ultimately, you have religious motivations (Amarr/Matari) and humanist motivations (Gallente/Caldari) with each empire's end goals simply being what they view as the ultimate existence for themselves and humanity as a whole.
At least, that's my very limited understanding from my very limited time in EVE.