The secondary progressions are the most popular system of natal chart progressions.
The basic formula is "a day for a year". That is, in this predictive technique we consider that the planets' movement in a day represents the movement of the progressed planets in an year. For instance, if one wants to have a look at the secondary progressed chart of someone of 30 years, that will be represented by the planets' position 30 days after birth. Pretty easy.
The amazing thing is that this stuff works. And it works very wel in predictive astrology. Why would that be? It is generally explained as a symbolic link between a day and a year, the Earth and the Sun, Matter and Spirit. This is the world we live in: all full of symbols.
There are several other kinds of progressions as well. Tertiary progressions are based on the "a day for a month" formula, on the relationship between the Earth and the Moon, the Matter and the Soul, while minor progressions are based on the "a month for a year" formula, on the symbolic Moon-Sun relationship, the Soul and the Spirit.
In everyday astrological practice, most astrologers stick to the secondary progressions. Significant life events will occur when a progressed planet changes sign or house. The aspects between the secondary progressed planets and the natal planets are also relevant.
As the outer planets (Uranus, Neptune, Pluto) move very slowly in a day, the progressed outer planets will move very slowly in an year, making them useless to prediction, so they're never used. By contrast, the Moon moves quickly about 12 degrees/day, so the the secondary progressed Moon will also move at a rate of about 12 degrees/year, that is 1 degree/month.
While the general interpretation of a transit (for instance transiting Sun conjunct natal Mars) is similar to that of a progression (such as secondary progressed Sun conjunct natal Mars), there are two main differences that we should higlight: the progressions are totally personalized (while I have secondary progressed Sun in Libra, my wife doesn't, but we're both under the influence Saturn's transit through Leo) and second the progressions last longer, meaning that their influence will be less obvious but stronger in the long run.
The progressions represent the unfolding of the natal chart's promise in this lifetime. They're as unique as the natal chart. They are part of our destiny, just as shown by the natal chart. The progressions represent our personal transformation, while the transits represent our interaction with an evolving world.
Bernadette Brady says that the progressions represent "the way the cosmos manifest through us, as compared with a transit, which manifests on us".