Tachanun (תַּחֲנוּן) is the noun for supplication — an earnest, humbling plea for grace. It derives from the root chanan (to be gracious, to show favor). To offer tachanun is to acknowledge one has no claim on God's favor and to appeal entirely to His mercy and grace. The word appears frequently alongside tefillah (prayer) — distinguishing the petition element that acknowledges grace.
Daniel 9:3-20 is the supreme OT example: Daniel sets his face to the Lord in 'prayer and pleas for mercy (tachanumim),' confessing Israel's sin and appealing entirely to God's great mercy (9:18: 'We do not present our pleas before you because of our righteousness, but because of your great mercy'). Zechariah 12:10 promises God will pour out 'a spirit of grace and pleas for mercy (tachanumim)' on the house of David — a messianic mourning that becomes the fountain of salvation. Tachanun is still the name of the Jewish daily penitential prayer said on weekdays — a direct continuation of this biblical tradition.
Tachanun is the posture of pure grace-dependence. Every authentic prayer contains it — the recognition that we approach God not on the basis of our merit but His mercy. The promise of Zechariah 12:10 connects this supplication to the cross: when Israel looks on the Pierced One, the spirit of tachanun — grace-seeking, mercy-pleading — will be poured out. The new covenant brings not just forgiveness but a new heart that longs to approach God in humble, earnest supplication.