Look at sprinters, lean and mean,
None need belts to hold up their jeans;
Contrast with the sight of a plumber's crack,
Surely an unpleasant view from the back;
I say, tilt your pelvis to the back,
But won't that put the spine out of whack?
Never fear, your spine's meant to curve,
From the side it wiggles and swerves;
Use your glutes, not your quads, they're your biggest muscles,
I tell the truth, this is no hustle!
So tilt your pelvis, stretch those glutes,
You'll quicken your movement, sabaki, and shoots!
First, I apologize for the poem.
Next: what is anterior pelvic tilt, you ask? Okay, stand up. Put your hands on your hip bones - just below and to the sides of your belly button. Now kind of arch your lower back a little and try to stick your ass out. It may help to turn your knees inward (to get the feeling). That's anterior pelvic tilt. Next, turn your knees out and tuck your ass under you. If you're a guy it's the way you'd stand to pee in the woods - imagine you're trying to push your crotch forward ahead of you. That's posterior pelvic tilt. When your pelvis is sort of in the middle - tilted neither way - that's neutral.
Now let's start off by being clear: too much pelvic tilt in either direction isn't safe. Extreme tilt puts the spine into a compromised position and I'm not recommending it. Unfortunately, I can't give you specific parameters. If you feel discomfort you've probably gone too far. If you have lower back pain you've definitely gone too far - see a doctor or a physical therapist.
In karate the traditional advice is to adopt some posterior pelvic tilt. Proper form for most stances includes "tucking" the pelvis under. The usual explanation is that this straightens the spine or engages the anterior core (the core muscles in the front of your body). I think this is a mistake.
Look at some good athletes for a minute. Sprinters, Olympic weightlifters, even the most athletic fighters in MMA (George St. Pierre and Anderson Silva come to mind) - the guys who are best at moving around the cage. Now check out their hips (and I promise I mean this is the most non-sexually suggestive way possible). What do you see? They all tend towards anterior, not posterior, pelvic tilt. Their glutes stick out.
As for the spine, your spine is supposed to curve. This myth that you'll gain health or mechanical efficiency is based on the idea that your discs are flat, but two minutes spent with a model of a skeleton will show you that they're not. The discs are slightly wedge shaped, which means that for them to maintain optimal alignment the spine has to be curved the right amount.
So if we assume that some pelvic tilt is safe, why should we encourage an anterior tilt? What difference does the tilt it make? To answer that we need to keep in mind that motion at the hips is governed by a whole bunch of muscles. The glutes, hamstrings, quads, and a host of other muscles work in concert to move the hip. Changing the angle of the pelvis will change the relative contribution of these muscles.
You can feel this happening. Find a staircase. Climb the stairs two, three, or four at a time, depending how tall you are. Try doing a flight or two with your pelvis tucked under into posterior tilt. Feel where the strain focuses. Then climb a flight or two with yoru pelves stucking back - anterior tilt. You should feel the thighs (quads) working a lot more with posterior tilt and the glutes more with anterior tilt. This is because anterior tilt slightly stretches the glutes, giving them a little extra purchase on the femur.
Simply put, anterior pelvic tilt results in increased use of the glutes. Why is that good? The glutes are bigger, stronger, and safer as the engine of movement than the quads and hamstrings. When the glutes contract the spine is protected and you move faster.
Want another simple experiment? Move forward and backward in front leaning stance (zenkutsu dachi). Take a few steps with each tilt - posterior, then anterior. Do the movements quickly, like you're really trying to drive into somebody standing in front of you. See which style gives you more speed.
There is another reason to maintain anterior pelvic tilt. When kicking to the side and high (as in a roundhouse or side kick to the chest or head) you might, depending on your pelvic structure, limit your range of motion because the knobby thing that sticks out of the top of your femur hitting against the bones of the pelvis (I did NOT major in anatomy). If you tilt the pelvis forward there is space for the head of the femur to slip behind the bone and you can kick higher. It's easier to feel this or see it than to read about it. Try to drop down into a full split with your pelvis tucked, then tilt it back and try again - you'll feel how the bones sit differently in the hips.
Want another experiment? Get into a fighting stance. Slightly tilt the pelvis to the anterior. Move around. If you don't feel any difference, try some glute activation exercises and do it again.
Another argument in favor of anterior pelvic tilt is this: it's sexy. How is that relevant, you ask? Well, it might be sexy by accident, or it could be that millions of years of evolution drove us to find sexy those traits that correlate with physical health and athleticism. Basically, all else being equal, a more athletic mate has a better chance to bear healthy children and keep them safe and provided for. So we'd be unlikely to find anterior pelvic tilt sexy if it didn't correlate with athletic ability.
To be honest, this is one of those recommendations that falls under the "not sure about and willing to be proven wrong" umbrella (along with intermittent fasting and explosive training, if you're keeping score). I know it works for me - I can feel the difference in my movement when I maintain a slight anterior tilt.
Try it out, next time you're sparring or doing forms.