Rulership
In Hellenistic, Vedic, Medieval and Renaissance astrology each house is ruled by the planet that rules the sign on its cusp. For example, if a person has the sign Aries on the cusp of their 7th house, then the planet Mars is said to "rule" their 7th house. This means that when a planet is allotted a house, its nature comes to have some bearing on that specific topic in the person's life, and that planet is said to be very important for events specifically pertaining to that topic. The placement of this planet in the chart will have at least as much influence on the chart as the planets within the house. In traditional Western & Hindu astrology, each sign is ruled by one of the 7 visible planets (note that in astrology, the Sun and Moon are considered planets, which literally means wanderers, i.e. wandering stars, as opposed to the fixed stars of the constellations).
In addition, some modern astrologers who follow the X=Y=Z or Planet=Sign=House doctrine, which was first taught by Alan Leo in the early part of the 20th century, believe that certain houses are also "ruled" by, or have an affinity with, the planet which rules the corresponding zodiacal sign. For instance, Mars is ruler of the 1st house because Aries is the first sign, Mercury rules or has an affinity with the 3rd house because Gemini is the 3rd sign, etc.
This highly oversimplified concept is sometimes referred to as "natural rulership", as opposed to the former which is sometimes called "accidental rulership." It is problematic when we consider that Neptune is not a planet that rules any sign under the ancient rules, because it was not known to the ancients.
The theory of "natural rulership" of a house is also challenged by a document from the Hellenistic era called the Thema Mundi, a teaching chart the name of which translates to the chart of the world. This chart has Cancer in the ascendant, which suggests that the astrologers from whom we inherit most of our astrological knowledge were proposing that the 1st house is associated with the sign Cancer. Astrologer Eric Francis has described this as the "90-degree shift issue."
Read more about this topic: House (astrology)