When I first started learning pilates in high school, one of the larger points of discussion was pelvic placement. In the classical pilates community, a tucked pelvis was traditionally taught, because that's how Joe Pilates taught. In the contemporary communities, neutral pelvis was encouraged with the idea that Joe would have continued refining his alignment based on available knowledge.
In his books, Joe's ideas about the spine were that the healthiest spine was the one we are born with...a full C spine. But we develop what are called secondary curves as we go from an infant to a toddler, able to walk, run, climb and explore. These secondary curves are in our lower back and in our neck spines and curve in opposition to the upper back, sacrum and skull. That's how we get the stunning, architecturally efficient, shock absorbing S spine. And this is what contemporary teachers started pulling into their practices.
The pelvis and the spine are eternally interconnected. They are partners (for better and worse) and they often have to deal with our environment that isn't necessarily built for the variability in spines and pelvices, nor for best placement. Gravity is also always at play which can be helpful for grounding, but sometimes difficult to work with.
A neutral spine is exactly what it sounds like. It is in the middle...in between the extremes of tucked and tilted. In standing it creates a strong support for the organs of the body while also providing the foundation for the spine to weave upwards with equanimity. But to know neutral, you need an understanding of the extremes.
A tucked pelvis is also called a posteriorly rotated pelvis. This is where your tail curls underneath you, your lower back rounds and your abdomen caves inwards. In this posture the pelvic floor generally shortens, the gluteals engage, and the abdomen engages. Conversely this opens the hip flexors and lengthens the spinal muscles.
A tilted pelvis is called an anteriorly rotated pelvis. This is where your tail reaches back a bit, your lower back arches, and your abdomen moves forward and lengthens. In this posture the pelvic floor generally lengthens, the hip flexors engage, and the spinal muscles engage.
As with all practices, creating the space to make a choice rather than following habit is the goal. Your pelvis can inhabit many different positions and should be able to do so, and then move to another position. Knowing where neutral is, when to utilize and and how to move into it when there is resistance is a skill that can take some time, but well worth the practice.