Chord progressions are a sequence of chords played in a particular pattern in order to harmonize the melody. They are used to form the basic framework of a song. In most cases, chords share at least one note with the next chord in the sequence.
Chord progressions are based on a particular scale, and the notes of each chord are usually taken from the notes of that scale. The most frequently used chord progressions are based on the first, fourth, and fifth scale degrees. The first degree is referred to as the tonic, the fourth is called and subdominant, and the fifth is labeled the dominant.
These scale degrees are most often written as roman numerals. The tonic is written as a I, subdominant as a IV, and the dominant is the V. To differentiate the difference between major and minor chords, lower and uppercase roman numerals are used. Uppercase roman numerals such as IV and V denote major chords. Lowercase roman numerals such as ii and vi refer to minor chords.
One of the most basic chord progressions is the I-IV progression. If you were to play a I-IV progression in the key of C, you would first play a C chord followed by an F chord. In the key of F, you would first play an F chord followed by a Bb chord.
Another example of frequently used chord progressions is the ii-V-I sequence. This progressions is very popular in jazz music. In the key of C, you would play a D minor chord, followed by a G major chord, and end on a C major chord. In the key of F, you would first play a G minor chord, followed by a C major chord, and finally an F major chord.
There is a virtually unlimited number of chord progressions you can come up with. If you want to learn how to improvise on the piano, learning a variety of chord sequences is a great place to start. Only your imagination will be able to hold you back after that.