Time Under Tension (or "TUT" for short) is a training method which focuses more on how much time you spend performing your exercise, rather than how many reps you can do per set or how much weight you can lift. In theory, the longer it takes you to perform each set, the longer your muscles are actually being used. And the longer you spend actively engaging your muscles in strength-building activities, the more likely you are to build larger, stronger, leaner muscles.
But it's not all about working out in super slow-mo. TUT enthusiasts believe that there is a specific amount of time you should spend performing each set based on what you actually want to accomplish during your workout. If you're focused on muscle endurance, then by all means, aim for about 70 seconds of TUT per set. If you want to be the biggest meathead in the weight room, then you'll probably set a TUT goal closer to 40 seconds per set. And for a small yet deceptively strong musculature, try for sets that are less than 20 seconds total. Keep in mind, these are very broad estimates. Rep and set times will vary based on any number of factors. Those factors can include such things as the specific exercise you are performing, the amount of weight you are using, and more.
Like any bodybuilding technique, most of the evidence which supports TUT training is anecdotal. It also flies in the face of the classic BroScience training techniques favored by old-school gym rats who get as much pleasure watching themselves flex in the mirror as they do bragging about exactly how many pounds they can bench. These Brofessors love to keep it simple, and insist that the only thing that matters as far as getting bigger muscles is answering the "how much/many" questions: how much can you lift? How many reps can you do? How much have those numbers increased over time? And if your answers aren't constantly coming in the form of bigger and more impressive numbers, then (according to them) you aren't making any real gains.
However, when you get right down to it, people who insist that their way is right and any other way is wring are forgetting two very important facts:
So experiment here and there, keep varying up your training routine, and do what works best for you.
And also: try Growth Factor.