The reason why there are so many different House systems used in Astrology is because some astrologers try to take into consideration those individuals who are born far away from the equator, namely close to the North & South Poles.
2 of the most impt aspects to be considered in the chart are the Ascendant & MC whi are exactly at right angles (90 deg apart). On the Equator, the Asc & MC will always be at right angles to eahc other but the further one goes to the North or South, the angle will vary drastically.
It is important to understand that even though the house cusps are irregular in these other systems, the space they represent is regular. This is because although the chart is presented on flat paper, it is in fact a three dimensional sphere.
The most popular House systems are as follows: -
Equal House System
To 'correct' the problem, the oldest and most popular form of Hose system - the Equal House System - is most often used. Every House is divided into 30 degs and once the starting point is always the Ascendant. Once it's calculated,
one simply divides the rest of the chart using the Ascending degree as a starting point.
Placidus House System
This is an unequal house system. Depending on the latitude used, a Placidus chart may have entire signs contained in a house, known as intercepted signs. As with most unequal systems, charts drawn for higher latitudes often have houses that are either very small or very large, with houses being more "equal" in size, the closer to the equator the latitude for the chart is.
Koch House System
This is a relatively new unequal House System used to generate the most accurate house cusps, especially for forecast timing using planet transits to the natal chart. It is becoming more popular with astrologers inr ecent years.
To sum up, the difference between the various house systems is mainly the actual degree and minute on the house cusps according to the Tables of Houses used to generate the calculations.