To punish or reprimand by forcing to do intense physical training, often until the individual or group being smoked can endure no more.
Back in Basic, we got smoked a lot. The first smokings I got were outside on the paved lot between reception barracks. For some reason there were tiny loose rocks forming a thin layer on top of the pavement. If it weren't shipped in from some mine where Drill Sergeants hand picked the sharpest, smallest rocks, I'd be surprised.
We'd be out there in the heat of the Missouri spring day (having been out there since the cold of the Missouri spring morning). The pavement's heat on our hands was unbearable. This huge paved lot's only job in its recent life was to soak up and distribute the sun's rays to our welcoming hands, and it deserved a promotion. Our hands were sore throughout all of reception. And that wasn't the worst of the smokings.
After reception, when we were actually in the midst of basic training, our platoon did our Physical Training (PT) in the tin can. This structure had three walls and a roof. The floor was probably a few feet lower than the ground around it. In this space was placed minced rubber tires. At first, and for the most part, we thought this was rather considerate; it kept the sun off our backs (or fronts, or whatever wasn't currently in contact with the ground) and it was somewhat cushioning and forgiving when we hit the ground hard.
The one tin can session that sticks out was a group smoking - four or so of the fifty in our platoon had done something wrong - I don't remember what it was. Looks like I didn't learn that lesson, eh? Anyways we front, back, go'd, did somersaults across the length of it, bear crawled, low crawled, high crawled, POW crawled, and much much more.
From the Drill Sergeants' point of view, I then saw the mission of the tin can. It heated up instantly, and kept the dust we kicked up concentrated. We were breathing hot dusty air, getting caked with dirt from sweat and dust, and generally having a miserable time.