Domine, non sum dignus - how to say it and roughly what it means

3:35 - we finally say it through slowly as originally requested.

This question arises when you start going to a Latin Mass - just before Communion, the priest turns around, holding up the Blessed Sacrament, and he says: "Ecce Agnus Dei, Ecce qui tollit peccata mundi" and then the whole church erupts in a usually rather mumbled version of "Domine, non sum dignus ut intres sub tectum meum, sed tantum dic verbo et sanabitur anima mea." (once at a Novus Ordo Latin Mass, three times for those using earlier ordos)