What are different astrology house systems about?

The houses of the horoscope are shown in the chart wheel as "pie" shaped divisions.
The 12 houses in a chart are determined by the exact clock time of birth. The houses represent a more physical plane area of of life, whereas the sign describes an approach.
For example: the 7th house is marriage and partners.
The sign Libra acts diplomatically and seeks fairness and justice.

There are at least a dozen or more house systems used by astrologers according to personal preference. Given below are explanations for the most popular of these.
The following paragraphs are condensed explanations of the various house systems offered at Sky View Zone.

Equal House System:

A simple, yet highly effective system, this was the method that the ancients used before the various unequal houses systems developed. Any table of houses may be used because once the ascendant degree is discovered, the divisions of the chart wheel are equally divided with the same degree as the ascendant on each house cusp. The signs on the cusps then follow in order around t he wheel beginning with the rising sign. There are no intercepted signs in equal houses and therefore each sign is represented on a particular house cusp. The Equal house system does not create very large or small houses that become even more pronounced the higher the northern or southern latitudes used to calculate the chart.
-The Equal House System avoids the problem with the Placidus which results in extremely uneven houses if the native should be born in extreme northern or southern latitudes.
-Each sign is fully represented on a house cusp.
-Debbie Kempton Smith the author of Secrets from an StarGazer's Notebook recommends either Equal House or Koch (unequal).
-Margaret Hone puts forth an excellent argument in favor of Equal House in her book, "Applied Astrology" which is why it is the default for SkyViewZone.
Jeff Mayo and the Faculty for Astrological Studies also favors this house system.
http://www.solsticepoint.com/astrologersmemorial/hone.html

Placidus House System:

Developed by Placidus (c.1688) and long popular for it's intrinsic value, the Placidus house system came into wide favor because for a long time the Placidean Tables of Houses was most easily obtainable.
Placidus 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:

A house system developed by Dr. Walter Koch that is considered by many unequal house advocates to generate the most accurate house cusps, especially for forecast timing using planet transits to the natal chart. First presented in 1964, Koch is one of the newest house systems quickly gaining favor with astrologers. The same intercepted signs and unequal divisions occur as with most unequal house systems. 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.

Sun-on-the-ascendant; a.k.a. "Solar Chart":

This house system is used when the time of birth is unknown. Rather than just creating a natural chart beginning with Aries on the Ascendant which is basically a futile exercise chart-wise, the Sun-on-the-ascendant method simply uses the individual's Sun sign and degree as the chart starting point; in other words the cusp of the first house. The rest of the planets are then placed into the resulting houses as usual. The information derived, is about 65% to 70% accurate with respect to the individual's life experience as far as the planet in house interpretations. All other planet in sign and the aspects interpretations remain the same as a regular chart reading as far as accuracy. The exact Moon sign and house placement is most at risk for being "off" when the birth time is entirely unknown, because the Moon is by far the fastest moving factor and it's quite possible that it may have changed signs at some point on the date on birth. It is definitely better to use this system for unknown birth times with an awareness of the drawbacks, rather than create a false chart using one of the above house systems. The chart is then read mostly with an emphasis on the characteristics of the Sun, since the Sun is considered to be such a major chart factor, especially in western astrology.