The heart of the matter is logistical, rather than anything else.
From the Imperial perspective (that is, the perspective of the Adeptus Terra, as the government of the Imperium of Man), the smallest discrete element of territory is the world.
An individual world is ruled over by an Imperial Commander - also sometimes known as a Planetary Governor - who rules that world on behalf of the Imperium. The Imperial Commander has basic obligations to the Imperium - the provision of a tithe of men and materials (the quantity and composition of which are determined in exacting detail by the Administratum), the collection of psykers, the maintenance of a standing armed force for planetary defence, and so forth.
A star system may or may not have multiple inhabited worlds. Where multiple inhabited worlds are present in one system, one of them will be regarded as the primary world, to which all others are beholden economically, spiritually, militarily and politically. The Imperial Commander of this primary world thus also has authority over the other inhabited worlds of the system.
Worlds are not, however, self-sufficient - they can be, but this is neither a requirement nor a defining factor. Multiple nearby worlds will be bonded by trade and mutual necessity in order to keep themselves supplied with essentials (food, potable water, raw materials, complex machinery, etc). An agri-world operates most efficiently with tractors and other machines to support the workforce, a hive world needs food for its populace and raw materials to produce machinery, and a mining world requires food to feed the miners and tools to gather materials… all three are interdependent.
The subsector can be viewed as an outgrowth of this concept - a cluster of nearby worlds, close enough that interstellar travel is not so long-winded, dangerous or arduous to allow for routine. As individual worlds cannot easily supply one another on a 1-for-1 basis, a complex network of interdependent worlds can form, particularly where one or more of those worlds produces a rare, valuable or unique resource. As with multi-world systems, one world in the subsector will be the capital, possessing authority and prominence over those around it.
A Sector, conceptually, is a cluster of several subsectors within a particular area - often defined as a cube a hundred light-years on a side. The stellar density within a Sector is immensely variable, leading to wildly-differing numbers of worlds per Sector depending on where you are in the galaxy and how established the Sector is. Within a Sector, individual subsectors will develop at their own pace, typically expanding outwards from the earliest colonisation attempts.
The most prosperous or otherwise prominent world within the Sector - typically a Hive or Fortress world, as they form a nexus of resource distribution and military power - becomes the Sector Capital. Sector Capitals are inevitably also subsector capitals, if only because it consolidates the logistics of the subsector and wider sector into one administrative entity.
Sectors are essentially autonomous entities - self-sustaining on a large scale, capable of significant military impetus (enough to support a crusade or territorial expansion), and able to exist independently of any external body save the Imperium itself. Each Sector maintains its own Imperial Navy Battlefleet (though these are nominally part of the Segmentae Battlefleets as well - for example, Battlefleet Armageddon is part of Battlefleet Solar), can muster untold trillions of Guardsmen, and possesses an extensive network of trade, religious and legal connections in the form of that sector's native Chartist Captains and embedded Adeptus Ministorum and Adeptus Arbites presence (whose structures parallel, but do not precisely mirror, the Adeptus Terra structures so far laid out).
The five Segmentae Majoris - Solar, Obscuras, Tempestus, Pacificus and Ultima - are the next level of authority, and only truly intervene in the matters of lower levels of organisation when utterly necessary. Few conflicts or crises ever expand beyond the potential capacity of a single Sector to deal with. When necessary, a crisis on a massive scale will be overseen by the office of the appropriate Master of the Segmentum (for the Calixis Sector, this is the Master of the Segmentum Obscuras, who commands from Cypra Mundi). The five Segmentum Capitals are Cypra Mundi (Segmentum Obscuras), Bakka (Segmentum Tempestus), Kar Duniash (Ultima Segmentum), Hydraphur (Segmentum Pacificus) and Mars (Segmentum Solar), and in each case these worlds are heavily-fortified worlds with massive manufacturing capabilities and extensive fleet yards (as always, Mars has the military and manufacturing infrastructure to support fleets and legions, while Terra is given over being the spiritual and metaphyiscal centre of the Imperium)
The Segmentae were originally defined for shipping and naval administration, but have expanded further in purpose as other organisations have taken advantage of the established infrastructure.
Ok… that took longer than expected. Hope it helps, though.