You have some correct answers re: what the blue canister is and about the hose that is not connected to it in the photos I see. That is part of the Fuel Evaporative Control System, one of those rare emission control systems that actually does good without causing any engine performance problems. RD-72 has provided some great information. I have attached a file with some more info, and a slightly different drawing that I think will add some useful perspective (see Pages 19 - 21 in the attached PDF file). Embedded in this post is a page from the attached file.
Further, I put together a YouTube video on our 1973 Mustang Convertible showing its different parts of the Fuel Evaporative System. That video is at:
The smaller rubber hose connects at the one end to a steel fuel vapor line that leads back to the top of the fuel tank where there is a liquid/vapor inlet valve. There is a larger diameter hose that also connect to the blue charcoal filled canister. If is made with a corrugated paper exterior shell, and a foil inner layer hose that leads to the air cleaner housing. You can get a replacement paper/foil hose from a few different places. Just Google on "1973 mustang fuel evaporative paper foil hose" - there is nothing magic about "1973," it is just what I used. You can substitute your model year if it is not 1973.
I urge you to get your Fuel Evaporative system connected back up like it should be. Otherwise you will be needlessly dumping fuel vapors into the atmosphere (unburned hydrocarbons), and you will end up with a garage filled with gasoline vapors, a situation that it totally avoidable and correctable.
