Suspension means to temporarily delay the resolution of one or more chord tones. Here, for example, is a C Minor Rootless Add2 (for lack of a better name) with its resolution:
This suspension sounds and feels particularly “bittersweet” because of the minor 2nd interval (D-Eb).
Notice how unstable and antsy the rootless add2 chord sounds and feels, like it needs to go somewhere, and how that instability is relieved upon the arrival of the minor triad.
Suspensions can be applied to add harmonic interest in many musical contexts. The most recognizable example may be Nadia’s Theme, which is based on a sequence of rootless add2 suspensions superimposed on a Cm-Bb-Ab-Gm chord progression.