What does mercy mean in greek?

The main Word for "mercy" as a noun is ἔλεος (e-le-os) and the Strong's Concordance gives its meaning as "compassion (human or divine, especially active):--(+ tender) mercy."

The main Word for "mercy" as a verb is ἐλεέω (el-e-e-o) and Strong's defines it as "to be compassionate (by Word or deed, specially, by divine grace):--have compassion (pity on), have (obtain, receive, shew) mercy (on)." The main form of this that's found is ἐλέησόν (e-lei-son) which is 2nd person imperative, meaning that it is a plea/request (for mercy) - this is what is found in the liturgical "Kyrie Eleison" (Kyrie meaning "Lord!" or something along those lines.)

Sources: http://www.zhubert.com/concordance and http://www.eliyah.com/lexicon.html