Progressions are one of the predictive techniques used by astrologers, applied to an individual's natal (birth) chart. There are several different types of progression techniques used, but the most common one is called Secondary Progressions.
Essentially, it uses every 24-hour period after the person's moment of birth to represent a year in their life. Whatever astrological events were happening in that 24-hour period reflect events in the person's life during the year that corresponds to that day. As an example, if the Sun changes signs 25 days after the person's birthdate, this indicates a significant shift in the way the person experiences and focuses their identity, vitality and life purpose at around age 25.
Secondary progressions are a much slower cycle than transits (where the planets are in real time). Often they have more of a background effect than transits which tend to produce more specific events (although every astrologer has their own perspective on this!)
It is considered very significant when a planet changes signs or enters a different house in the natal chart, which can show a significant shift in the way that person uses that planet's energy for many years to come. When a progressed planet forms a major aspect to a natal planet, it activates that natal planet in the person's life. And when a planet turns retrograde or direct by progression, this indicates a major change in how they experience and express that planet's energy.
Compare: Transits.