As far as I can tell a Holder is a feudal lord who holds territory in the name of the empire, from an estate to a collection of systems. That the title is used for all but the top few rungs on a long ladder seems to be the source of confusion. Lord and feudal lord appear in Myth of a Salesman and I don't think it's a stretch to say that it refers to Holders when compared to other PF, especially considering that it was written in 2002. A governor (note the lack of capital) is counted among a group of Holders in The Artifice Maker. Finally the heirs themselves are said to be a caste of Holders and are associated with holding large domains.
to the common Amarrian a Holder symbolized the grandeur of the Amarr Empire and to attack one was to attack the Empire itself.
At that time numerous minor Holders vied for power, each with his own ideas on how to run things. This resulted in a complex tapestry of rules and regulations regarding for instance education, travel permits and freedom of employment. With time this resulted in great economical diversity between the stations in the area, some prospered while others stagnated. When the emperor re-organized the administration in the sector a sole Holder was chosen to govern it as a whole, with governors on each station working under him.
The Amarr Heirs are the heads of the five royal families, the highest caste of the Holders apart from the Emperor family itself. Even if the emperor is the head of state his power outside his immediate vicinity is limited. The entrenched bureaucracy and the semi-feudal governing system means that all over the empire there are local lords that enjoy almost complete autonomy most of time. The Heirs are the most powerful of these lords. Each heir family has vast domains spanning dozens of solar systems.
That's not to say there isn't flexibility here. It's very reasonable to assume that a Holder may have domain over something other than or in addition to territory, such as a service or industry. It's a big empire. In reference to slavery I don't believe it has any real relation to Holders other than most Holders having slaves amongst those they govern. Slaves are traded and bred openly in the empire and during this ownership likely passes through many people who are not Holders. It is possible they remain under the nominal ownership of a Holder unless released from the Empire, though at that point it becomes mere semantics.