On a normally-proportioned person, the center is located along their line-of-symmetry (thus, "the centerline"), at a point halfway between their navel and their waistline, and roughly halfway inside their body. The Japanese call this point the hara; the Chinese call it the tan-t’ien. According to Traditional Chinese Medicine, the center is a “lake” of ki, which feeds life-energy to the rest of the body through a series of tributaries ("meridians"), just like how a car's master cylinder compresses brake fluid. Likewise, since the center is said to be the exact physical location of the immortal soul, it is one of the body’s seven chakra, and several energy vortices. In Goshin-Jutsu, we ignore all of these things -- not because they have no verifiable basis in reality -- but because they have no practical application if they did.
We use the term “center” to help divorce ourselves from mysticism. The center is merely where the body's center-of-mass is located. From a physics standpoint, people can be treated as a single dot, weighing as much as a person, floating at that point in space. As a teaching tool, the knot of a karate belt corresponds to the center's location on a normally-proportioned karateka. When your belt's knot is below your opponent’s knot, then your center is lower than your opponent's center. Then, you will have leverage, and the resulting mechanical advantage will multiply your strength.
[picture of a karateka being reduced to a dot]