Decay is the setting that expresses how long the tail of a reverb takes to fade away, or how that fade progresses. Most reverbs show it in seconds. Longer values extend the tail, and shorter values let the reverberation settle sooner. Decide it not only by how a source sounds on its own but by how it overlaps with the following notes and with the other instruments.
Characteristics of long decay
Long decay makes it easier to create the scale and the sustain of a large hall. On the other hand, it easily turns muddy when chords, lyrics, or fast phrases overlap. If you want a long tail, it helps to reduce the send amount, cut the low end of the tail, and take the gaps in the performance into account.
Characteristics of short decay
Short decay adds a sense of room and thickness while keeping the outline of the dry sound. It tends to be easy to work with on drums, rhythm instruments, and fast songs. Make it too short, though, and the tail can cut off unnaturally, or it can feel as though only the tone has changed.
Relationship to tempo
Matching decay to the tempo makes it easier to predict how much of the tail carries into the next beat. You do not have to match the seconds mechanically, though. Judging by the arrangement matters more: longer where the song is sparse, shorter where the density is high.
How it differs from damping
Decay relates mainly to the overall length of the tail, while damping relates to how quickly particular frequencies, especially the highs, decay. Shortening the length alone also changes the character of the reverberation, so separate whether you want to darken it or to shorten the tail itself.
Points to check
Push the reverb a little hard once and listen for how far the tail carries. Then bring it back to the amount the song needs. Basic operations including reverb time are covered in the reverb article.
