A suspension is a form of a chord, in the notation Xsus(4|2)y, where X is the name of the chord, 4 or 2 is the subdivision of the suspension, and y is any extra change, for example, 7th chords.

Suspensions are chords composed of the root and the 5th of a chord, plus the 2nd or the 4th, depending on the kind of suspension. 2nds usually resolve to a V first inversion (for example, in D Major, C# E A). 4ths usually resolve to the root (using the previous example, D F# A). Another note: suspensions only very rarely resolve to minor chords, instead preferring major chords.

Suspensions are most commonly used in classical music to add tonal color and emphasis on a cadence in a piece of music, and can sometimes be found tied to the chord that comes after it, called the resolution, with the 3rd sometimes found, in this case, slurred (rhyme for the most part unintended).

In Jazz and modern music, suspensions take on a different role. In Pop and New Age, double-4ths are common (in C, C F Bb), which are just VII chords in first inversion. Another way to visualize this: C D G (the VII, in this case) is equal to D G C (the same chord in first inversion, which became a I 4-4). Anyway.

Jazz uses suspensions that do not resolve traditionally as well, as Major 2nds are not considered entirely dissonant in some styles, allowing musicians greater flexibility and the discovery of new and exciting chords.