Psalm 8 marvels that God founds His strength on the weakest voices: 'Out of the mouth of INFANTS and of sucklings thou hast perfected praise, because of thy enemies, that thou mayst destroy the enemy and the avenger' (Psalm 8:2).
On the day after Palm Sunday, with the Temple courts in uproar — the money-changers driven out, the blind and lame coming to Him and being healed — 'the chief priests and scribes, seeing the wonderful things that he did, and the children crying in the temple, and saying: Hosanna to the son of David, were moved with indignation, and said to him: Hearest thou what these say? And Jesus said to them: Yea, HAVE YOU NEVER READ: Out of the mouth of infants and of sucklings thou hast perfected praise?' (Matthew 21:15–16).
The application is quietly enormous: in the psalm, the praise perfected from infants' mouths is directed to the LORD. Jesus accepts the children's hosannas as that praise — in the Temple, to the priests' faces — and lets the citation say what He does not spell out.