A quiescent letter is one that is sometimes silent.

In Hebrew, this is really just a way to think about the matres lectionis in order to wrangle them back into conformity with the rest of the syllable and vowel system:

The quiescent letter can be identified because it doesn't have a vowel attached to it. It makes no sound in itself, and doesn't count as part of the syllabification process, and can be thought of as being part of the preceding vowel (whether marked or presumed.)