Ashtakavarga (Ashta means eight and varga means division) is a system for assigning strengths to planets (Grahas) and Houses (Bhavas) for use in transit (Gochara) analysis, although it also finds use in natal chart interpretation. Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn and ascendant (lagna) participate in this system; Rahu and Ketu do not.

In the Brihat Parasara Hora Shastra, the basic reference for Vedic Astrology based upon Maharishi Parasara (the ancient sage who founded Vedic Astrology), ashtakavarga is described as a calculational method and a very powerful system that holds within it easy to use predictive tools. This commentary also suggests that there is a deeper understanding on which ashtakavarga is based upon and that perhaps holds even more profound knowledge.

Ashtaka means 8, and refers to the 7 primary planets (grahas) + lagna which contribute to the ashtakavarga calculations. The basic principle is that from each house of a planet, certain houses (bhavas) benefit, or receive strength. Although it is tempting to do so, we will avoid judgemental terms such as good/bad or benefic/malefic, as their meanings are somewhat ambigious. For example, falling down and scraping your knee might be considered undesirable, but not so if you found a gemstone as you were getting up.
There are many types of ashtakavarga. For example, we can speak of the ashtakavarga of each graha and lagna individually, and the combined ashtakavarga of the seven primary grahas.

One of the main uses of ashtakavarga is in transit analysis.

Sarva Ashtakavarga

Sarva means sum or total, and sarva ashtakavarga is the value arrived in each bhava (house) by adding the contributions from each graha. A controversy exists as whether or not to add the contribution of the ashtakavarga of lagna. This is generally not done in keeping with Parasara, and is not used by most astrologers. Nevertheless, there are differing opinions on this matter. Excluding the ashtakavarga of lagna, the sum of the sarva ashtakavargas over all 12 bhavas is 337.
The sarva ashtakavarga is a very simple and useful tool for transit analysis. To gain positive results an average value of 25 points is sufficient. Some general guidelines about using the sarva ashtakavarga are:

1. Grahas in signs where the sarva is between 15-20 have little effect
2. Grahas in signs where the sarva is between 20 and 25 (inclusive) have moderate effect
3. Grahas in signs where the sarva is between 25 and 30 have a good effect
4. Grahas in signs where the sarva is over and above 30 have a very good effect

Note that if a graha has moderate to strong effect on the sign it is in, this also affects the signs it aspects. If the sarva is weak but the ashtakavarga of the graha of the sign it occupies is large (4 or above), then its effect on the sign will be felt. If both the ashtakavarga of the graha and the sarva are small, then the effect is weak. If both are large, then the effect is large. If one is weak and the other strong, the graha can still have a strong influence on the sign, depending on the size of the graha ashtakavarga and sarva values.
Take the above as guidelines, rather than as absolute rules. As you interpret more charts and see for yourself how the ashtakavarga correlates with life events, you will develop a good "feel" for their use.