Sociological: Omni declares himself a Nephite, and that he has personally fought to preserve his people - the Nephites - from falling into the hands of the Lamanites. We also have his personal admission that he is not a man who follows the ways of the Lord. Of course we get the "as I ought to have done" because of the permanent record.
What may we understand from Omni's brief description? First the obvious, that there are increasing numbers of wars with the Lamanites. Conflict has been a major sub-theme of the small plates from the time of Nephi, and we will see it continue. Secondly, it should be very clear that Omni's use of the term Nephite is absolutely political. That is, he is a Nephite because of his allegiance to his community, not because of his religion. He is also a Nephite due to lineage, and Jacob (in Jacob 1:13) does indicate that there is a continuation of clan designations, but Omni is using the term in the wider collective sense ("my people"). He is fighting not for a clan, but for the political collective called Nephites under the wider usage Jacob had indicated.