The new (canon) novelisation of Star Wars: A New Hope indicates clearly the the blast-helmet belongs to the ship and was clearly not intended as a Jedi training device.
The old man rose to his feet, smoothing his brown robes as he searched
the hold for something. Ah—a helmet.
“I suggest you try it again, Luke,” he said, placing the large white
helmet on the kid’s head. Its blast shield was down, effectively
The "blast shield" appears to be precisely that, a shield that can be folded down to protect your eyesight from the visual effects of bright lights such as plasma explosions or flying toward a sun while still providing a small amount of normal visibility.
The Radio Play describes it thusly:
Kenobi : Here, we'll start with you wearing this flight helmet. Now, lower its blast shield into place.
Luke : With its blast shield down like this, I can hardly see
As you can see from the images below, the markings on the helmet (and indeed the prop itself) match a pilot's helmet that was edited out of a later scene and used by a female x-wing pilot. In place of the smoked plasteen blast shield, she has a yellow anti-glare eye shield. This could be evidently be removed by sliding it up into the body of the helmet.
Since the helmet is of a modern design it seems more likely that the helmet belongs to Solo rather than Obi-Wan. That said, given that it was (according to the Junior Novelisation) being stored at the "Engineering station" and given the extensive weathering on it, it certainly seems possible that Solo and Chewie were also using it for welding rather than as a pilot helmet.
The authors of the Star Wars: The Essential Guide to Warfare apparently considered including an extensive description of the use (and misuse) of the helmet blast shield in their book:
A day before the third hop, they collected our helmets and brought
them back with blast shields you could flip down over your face. I’d
like to meet the glit-biter that put these things together — the
shield was huge, and when I flipped it down the hinge practically
pushed the bridge of my nose back into my skull. They told us to keep
the blast shield up until it was time to fire the charges, snap it
down, then pop it back up when the flash had dissipated. They said
next hop they’d wire a HUD in there, but for now it was just plastoid.
The fold-down 'helmet blast shield' is also mentioned in the EU book X-Wing: Rogue Squadron
Suddenly the starfield went black and the simulator pod hissed as it
cracked open. The canopy lifted up and the sound of laughter filled
the cockpit. Corran almost flicked the blast shield down on his helmet
to prevent his three friends from seeing his embarrassed blush. Nope,
might as well take my punishment. He stood and doffed his helmet, then
shook his head. “At least it’s over.”