Hi Maria,
The Arabic Parts are calculated points used in the delineation of charts and in divination.
They are a later version of the Greek Lots - 'Lots' in the sense of drawing lots. Although the Greeks appear to have used a fairly limited set of Lots, the medieval Arab Astrologers increased the number to well over 100, so I'm going to confine myself to a few general comments. In all cases we calculate the distance between two positions (planets, points, other lots) and add this distance to a third position (again planet, point, or other lot)
For some Lots, the calculation is a little different depending on whether the chart was cast for a time during the day (Sun above the horizon) or during the night (Sun below the horizon). The Greeks called this 'sect' and the day sect is ruled by the Sun and the night sect is ruled by the Moon.
Many Astrologers still use the Lot of Fortune in chart interpretation - it originally related to a person's body and physical health and as wealth was often determined by our health, it also came to include our material wellbeing.
The Greeks and Arabs calculated this as:
Distance of Sun to Moon by Day added to the Ascendant
Distance of Moon to Sun by Night added to the Ascendant
The modern (but still gives the same result) is
Asc + Moon - Sun during the Day
Asc + Sun - Moon during the Night
A lot of modern Astrologers ignore the difference and use the day calcuation for both night and day charts. Indeed the Lot of Fortune is the ONLY Lot still in common use. However there is a growing group of Astrologers that are exploring traditional methods and they do use some of the other Lots.
Other ones of Note are:
The Lot of Spirit - this is the 'mirror' image of the Lot of Fortune - i.e. the Lot of Spirit by Day = Lot of Fortune by night (In terms of calculation). The Lot of Spirit is used for information about our mind and soul - the non-material side of life.
There are also a series of Hermetic Lots, which use the Lot of Fortune or the Lot of Spirit together with the positions of one of the other planets (Mercury, Venus, Mars, Jupiter and Saturn). If you are interested in Hermeticism and its origins these may also be of interest to you.)
Other Lots deal with marriage and family relationships.
All lots are interpreted according to the condition of their ruler (Planet ruling the sign they are in), their House position, and aspects to them (this is the least important of the three).
If you like I can give you a longer and more detailed explanation but I'm assuming here you just want a general answer.