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"Stay tight!" is common to hear in lifting gyms. What it refers to is tensing the necessary muscle and when it comes to powerlifting it means pretty much all of them. The more tension your body creates, the more stable it will be when lifting. It will also make you stronger, even when focusing on tensing muscle that to an outsider doesn't seem to matter. An example of this is gripping the bar hard when bench pressing. Tension is “contagious” and the more you tense up the stronger you will be.
As you will see later in this manual, "tightening up" happens already before you unrack the barbell. It's that important. Depending on the movement, tension is more or less important. For instance, in Olympic weightlifting it's not a good idea to tense your entire body as it might slow you down. In powerlifting it's a different story. In the bench press, for instance, the focus should be staying very tight unracking the bar and tense up even more when lowering it.
Due to, well, physics, the faster you lower a bar, the faster you will be able to lift it if all things are being equal. All things are however not typically equal. Lowering the bar fast in squat or bench press often result in a loss of tightness and control which can result in a worse lift. Therefore always remember that tightness is more important than speed. Don't actively slow down, go as fast as possible (which in reality might be fairly slow) without sacrificing tension.