Anatomical spinal extension is the spine in its normal position when you're standing. The lower back has a slight curve forward and in.
A "straight" spine is something different. If the lower back is straight, the lumbar spine will actually be slightly flexed. In most cases that's okay. Greater flexion is not okay.
You need a bit of time watching people's backs as they lift. The deadlift is a good one to watch, as the lower back position is much more obvious than in the squat. When they go "chest up!" you'll see their lower back go into extension, so that it's much as in the standing position, curved forwards. When they begin the pull, often their lower back will go straight. That's usually okay. But if it flexes further then it becomes rounded - not okay.
Here are some examples.
First, the spine in anatomical extension (ie lower back curved in forwards)
Next, the spine in anatomically neutral extension. Not curved in as it would be when the guy's standing, but not so flexed as to be a problem for him.
Okay, now we have the spine flexing, as we go from one image to the next it gets worse.
Once you've got the idea of lower back position in the deadlift, you'll see things more easily in the squat. It's a matter of degrees. Lifting weights ain't ballet, but we want it to be safe and effective. A fully extended spine is safe and effective, a neutral spine is safe and effective, as you flex the spine more it becomes less safe and effective.