Not too sure which one you mean, theres three in the pic and a yellow line...The fatter one kind of looks a bit like the vacuum hose that goes to the brake booster, especially with that valve in it, if it is I have no idea what its doing all the way up the front, routed like that.
I would be inclined to think its something to do with the emissions stuff, any idea what each end is hooked up to? - if it is emissions stuff and if no one's looking...rip it out...your car will go better!
It also looks like your car has the original fuel lines wrapped in the cloth braiding. The braiding hides the cracked rubber beneath..I think it would be a good time to replace them considering you can smell petrol
