Kinot are the elegiac poems and lamentations that we say in the synagogue on Tisha bAv. They are usually recited while sitting on the floor or on low stools as a sign of mourning for the destruction of the Temple and the subsequent tragedies in Jewish history which are connected to Tisha bAv.
Kinot that were composed in the wake of these events have been continuously added to the liturgy. As well as laments over the Temple, there are also kinot inspired by the Crusades, the York Massacre of 1190, the expulsion of the Jews from England in 1290, the Spanish expulsion and the Shoah.
Kinah means to wail, cry or lament. It is first used in the Bible when David mourns the death of Saul and Jonathan with the words, How are the mighty fallen (II Samuel 1:19).
In Jeremiah (9:16) we read of the mkonnenot, professional mourners whose job was to keen and wail at funerals to create an appropriate atmosphere. (Mkonnenot apparently also existed in other cultures at the time.)
The mourning of Tisha bAv is not meant as an occasion to wallow in grief, but rather to sharpen our yearning for the Temple and for a rebuilt and peaceful Jerusalem. The Talmud says that one who shares in the grief of Jerusalem will deserve to see its comforting.