The Seven Kingdoms of Westeros are divided between many hundreds of noble houses of various sizes. In Westeros ultimate power derives from the King on the Iron Throne and descends through the Great Houses that rule the constituent regions of the continent to their vassals.
There are nine Great Houses, and each of them have a number of vassal houses (sometimes also referred to as minor houses) in their liege. The most powerful vassal houses may themselves field armies of a few thousand and control large regions, whilst the smallest houses may be little more than impoverished landholders with only a few men to their name. Members of the nobility are called "highborn", in contrast to lowborn commoners.
A typical noble house is seated at a castle and controls the land around it, collecting tithes and taxes from farmers, lesser landholders and smallfolk. In times of war they are expected to recruit and maintain a number of soldiers for their lieges. In most of Westeros only men can become ruling lords, and women can only rule if the rest of the male line has been extinguished or if they are acting as regents for their sons until they become of majority.
In Dorne men and women have equal property, inheritance and ruling rights.
In the books
In the A Song of Ice and Fire novels and accompanying short stories, websites and RPG sourcebooks, there are over 300 named noble houses of Westeros. All of these are sworn to the Great Houses.
However, George R.R. Martin has admitted that his system of nomenclature for noble Houses isn't very precise, as major and minor lords are both called simply "lords" (as opposed to differentiating between "duke" and "baron" etc.) Each of the constituent regions of the Seven Kingdoms has about a dozen or so major Houses, i.e. House Umber is sworn to House Stark, rules a large area of the North, and several minor Houses serve the Umbers. House Cassel, meanwhile, is a minor House, sworn directly to House Stark, which has no minor Houses serving it. Thus there are roughly about 100 or so major Houses in the Seven Kingdoms at any one time, and numerous minor Houses who in turn serve them (not all of whom have been named).