Taken out of context, it sounds like typical "bro" logic (when people blindly accept what others have said just because they happen to be stronger). However, you'll find intensity defined differently depending on who you are speaking with. It can mean anything from simply "really hard" to the more precise meaning given in a strength training setting. However, with no link to the article, I can't speak directly to what the author was referring.
With strength training we have a few concepts with programming:
- Intensity: the heaviest weight lifted. Understood best in terms of your 1 Rep Max (1RM), is how close to your max did you lift?
- Volume: reps x weight. Basically, how much tonnage did you lift?
- Effort: Similar to volume, but expressed as a calculated 1RM.
In general, there is an inverse relationship between intensity and volume. In short, the heavier the weight, the fewer reps you will be able to lift with it. It does take less time to lift shorter sets (i.e. fewer reps per set). At the same time, your body does need a certain amount of volume to force it to adapt and get stronger. So managing the variables between rest and exercise is critical to getting stronger.
Now that the groundwork for terminology is laid, is there anything special about the 1 hour mark?
Only in that the longer your workout takes the more cortisol your body produces. That 1 hour threshold seems to be the optimum window to get your testosterone levels up without significantly increasing the cortisol levels. However it's still acceptable to have an hour and a half long workout. Much longer than that and it becomes counterproductive.
Working with heavy singles and doubles (sets that are 1 rep or 2 reps respectively), you can get your workout done more quickly. It may take a bit to recover from the training, but you got in, got it done, and went home.
Wendler style training has you focus on one major lift with assistance each training day. This lets you get the appropriate amount of volume and intensity, and keep the training to about 1 hour per day. The top set on the main lift is done for as many reps as possible. You compare your effort using the 1RM calculation so that you can track whether you are improving week to week or not.
Switching contexts for a minute here, when you are referring to conditioning work, intensity takes on a slightly different meaning. Essentially, it's how hard you are working. High Intensity Interval Training has periods of time where you are doing your max effort, with short periods of relative rest. The key to intensity is that max effort.
You can become much more efficient with your conditioning, and can cram 1 hour of steady state cardio into 12-20 minutes of HIIT with similar benefits. The trade off being long term endurance, vs. amount of Calories burned. Tabata training is one example of an HIIT protocol that lasts 4 very intense minutes, but yields a lot of good.
One factor that many people training forget to think about is the amount of rest between exercises and between sets. The longer you wait, the more rested you get (to a point), but the longer you training takes. The less you rest, the more the fatigue builds up. That extra fatigue adds to the feeling of intensity. One way of looking at it is the more fatigue builds up, the less your 1RM is for that level of fatigue.
Again there does need to be a balance. Training in a fatigued state can cause you to lose tightness, focus, and can increase chances of injury. Never let yourself go so far as to affect your ability to perform the exercise with proper technique. However, playing with that rest timer is an effective way to increase the training stress and volume your muscles need to adapt and get stronger.