Vacuum hoses...

Can someone please explain in basic terms what they do and how they relate to the fueling ?

I ask as I have recently had a few issues with the plastic ‘T’ pieces that join the vacuum pipe together snapping and wanted to understand how it all really works. Whilst the hosing is not complete, the fuel consumption went through the roof and the 5500 rev limit came in…

I’ve replaced the pipe, but had the replacement pipe split too…is there much pressure in this pipe ?

Thanks all !