Chullin 2 - Shechitah, Or Ritual Slaughter
Shechitah is ritual slaughter. It consists of cutting through the majority of the animal's trachea (windpipe) and esophagus (food pipe). This cutting is subject to a number of laws: it must be done from the front of the neck, in a continuous slicing stroke, and with a smooth blade.
All may do slaughter, and their slaughter is valid, except for a deaf-mute, a deranged person, and a minor - lest they bungle their slaughtering. But if any of these slaughtered with others watching over them, their slaughter is still valid. A minor is a boy before bar mitzvah, or a girl before bat mitzvah.
However, the teacher seems to be of two minds by allowing the slaughter upfront, and then validating it after the fact. According to Rabbah bar Ulla, this is talking about slaughtering regular meat on the level of purity required for sacrifices, since there were people who used to do that. Even a ritually impure person can perform this slaughter, provided that he uses a long knife and does not touch the meat, although initially he should not do it.
The Talmud will give five more possible explanations.
Art: Julien Dupre - A Shepherdess with Cows and Sheep in a Landscape