breather tubes question

["Evangelos G. Makris" <emakris@hol.gr>]

What are, ahem, breather tubes for? (breathing is something
that comes to mind, but what part needs to breathe and why?)

For example, there is a breather tube in my Mini SU HS4
that goes to a small black cylinder, what purpose does 
that serve?

There are other such tubes both in my 998 Mini and 1275 Sprite
and I'd like to know what they do, when can I tell they
need replacing, do they contribute to performance/economy?

Evangelos 
66 Sprite 1275
78 Mini 998