What is bellows looking thing on passenger firewall

[gramps77]

There is a plastic bellows looking thing with a larger vacuum line going to the engine and a smaller vacuum hose going into the firewall just behind the A/C and heater box. What does it do and is it important to replace that smaller hose going into the firewall with similar plastic type hose?
I think it may have something to do with the defroster cause my defroster had stopped cycling on and then I found this smaller line with a large crack/break in it.