In it's most simple definition, a Chord Progression is ANY chord that moves to ANY other chord. But, when we talk about chord progressions, we are usually speaking about those progressions which have been used time and time again to the point we recognize them to be "standard" progressions.
Standard progressions are used the vast majority of the time in tonal music and use the diatonic chords that are constructed from scale degrees which appear in the Major and Minor keys. These progressions can also establish "temporary keys" as the music temporarily moves in and out of other keys (see tonality for further information) and return to the main key.
Major Diatonic Chords: The 4 part chords that appear naturally in the major key (shown in C Major).
Minor Diatonic Chords: The 4 part chords that appear in the minor key (shown in A Minor).
Note: G# appears throughout and is from the Harmonic Minor scale used to create the V7 chord in Major (see E7 below)
Major Chord Progression: Shown using 4 part chords, but can be, and most often are, used with the basic triads without the Major 7th scale degrees. The first set of chords show a typical "IV-V-I" progression. This progression is the most used progression in music and therefore best established the tonal center of the music. The second set of chords show this same progression, but with a jazzier flavor. In jazz music, typically the progression will move in a "II-V-I" pattern as opposed to "IV-V-I". If we look closer, we same at the base of both of these progressions we still have the same chord tones. The "IImin7" chord is identical to the "IV" chord with the 3rd added to the bottom of the chord. The top notes of the "II" chord are the same as the "IV" chord. Using the "II-V-I" progression makes use of the strong root movement of the 5th (see circle of 5ths).
Minor Chord Progression: Shown using 4 part chords as well, but this time in the Minor key of "C Minor". Again note the use of G# from the Harmonic Minor scale to create the Major V7 chords. The functionality is similar to the Major Progression shown above and establish the tonal center for the progression same as it does in Major. Again we show this as "IV-V-I" as well as the "II-V-I" progression used most often in Jazz.
"I-VI-IV-V" Progression: Shown using 4 part chords again. Sometimes referred to as "Ice Cream Changes". A very popular chord progression used in many 1950s and 1960s ballads.
"I-IV-II7-V" Progression: This progression appears frequently in styles such as country. Notice the "II" chord has been altered by using a Major 3rd. This technically would be the use of a "temporary key" of "G", making the "D7" or "II7" temporarily act as a "V7" chord temporarily in the key of "G". Once we land on the G7 though, we are once again back to the original key of "C" as "G7" functions as the "V7" of "C".
Use of Temporary Key Progression: As stated earlier, in jazz and other types of sophisticated styles of music, the use of temporary key centers or tonics are used throughout a song. This means temporarily the key shifts to another key and the progressions temporarily function as progressions in that other key. Using the basis of the "II-V-I" progression which most defines a key to ear, we can see in the example below how music can use these temporary keys and arrive back at the tonal center, or tonic, of the song.
This page does not come close to covering ALL possible chord progressions. It is provided as a means to show the most effective common chord progressions which establish keys, and give an insight into establishing tonality along with the use of temporary keys in a song. Armed with this information, you will begin to see these reoccurring patterns in music, and be on the look out for more standard chord progressions. Extra information about strong chord movement can be found in the section of Circle of 5ths.