What's the purpose of it and what's the correct name for it I broke mines and can't figure it out, thank you in advance.

that hose goes to the thermac sensor on the botton of the air cleaner. that is the hose that opens the air cleaner up to fresh air. that line goes to one side of the switch and the other goes to the tbi.

here is a pic to go by

Thank you very much

Can I buy the hose by it self ,sorry for the dumb questions.

just take the hose to the autoparts and buy some vacuum line the same size/