It’s funny to me too, really. Like it doesn’t really change anything, but kind of changes everything at the same time. Adding weight to the bar is still the same. But all the times I’ve thought “I can lift X” has been a lie 
My commentary has always been far more unfocused than my training has. But I can give you a primer of what I’m trying to do.
On any given day we’ve got some amount of strength; some days it’s stronger, some days its weaker. Things like maxing out one day make us weaker on that same lift for a few days. Like we intuitively know that.
Now what’s cool is, if you measure bar speed while you try to lift the bar as fast as you can (not just at the beginning, but continuing to push as hard as possible the whole time), you get some useful information. A lighter weight you’re going to move faster than a heavier weight. (Again, common sense.) The first rep of a higher-rep set moves faster than the last rep. The first sets move faster than the last sets. You’re generally stronger/faster when you’re fresher.
So essentially you can use bar speed to measure how “strong” you are, in the moment, on any rep. It’s an objective measure rather than things like RPE/RIR.
If you take the time to personalize the formulas, you can actually measure the exact speed of a bench press rep and tell if that’s a 50%, 75%, 90%, 98% weight, just from the speed.
But what’s even more interesting is that those stay constant. So if your max is 135, and 50% moves at 1.0 m/s… when you’re stronger and your max is 315, 50% of that will still move at 1.0 m/s.
So, you don’t even need to max out to figure out what your 1RM is. You don’t need to do the approximation work like find a 3RM or 5RM and guess your 1RM from it. Or use a plus/AMRAP set. You can just measure the bar speed, plug it into a formula, and know what your 1RM is.
And that’s kind of a gamechanger for a few things… 1) you can actually see how your strength changes day to day, after a long weekend, after an all-nighter, etc., which is super informative and 2) it can completely change how your programming works, especially percentage-based programming
So, in my case, I’m basically doing “step-loading”. Stick with a weight until I’m “strong enough”. Then increase the weight.
Velocity makes it really easy to figure out when I can “earn” a weight increase. For my press, as soon as I can lift a weight 1.15 m/s, I can add another 5 pounds. For the deadlift, hit 0.66 m/s and I can add another 10.
Of course the math and formulas to get to the easy part are, well, complicated. But using it is easy.
