The section you cite is misleading. As Ignacio already said, the atoms in both P-type and N-type semiconductors are neutral. The difference lies in the distribution of electrons between valence band and conduction band.
In simple words: in N-type semiconductors there is an excess of electrons that are able to move relatively freely in the bulk of the crystal.
For P-type semiconductors the situation is reversed, there are less free electrons than in an intrinsic (i.e. undoped) crystal. This also enhances conduction, even if it seems counter-intuitive, since those "missing" electrons leave "holes" in valence band that can move as if they were positive charges.
To recap: doping enhances conductivity of the crystal by altering the equilibrium of free electrons with respect to the intrinsic crystal, not by putting more or less charges in the crystal itself.
Keep in mind that what I explained in basic terms is explained rigorously only by quantum physics applied to the crystal structure. Not an easy subject. I think even many undergraduate courses in electronics around the world don't delve into that subject too much. Even the concept of valence and conduction band cannot be explained quantitatively without formulas obtained from quantum physics.
I don't know your goals, but if you are an electronic enthusiast or an undergraduate student(*), usually you don't need to understand much more the subject to design electronic circuits and understand the external behavior of electronic components.
(*) unless you aim at becoming an IC designer, in that case you must know very well how the components behave "inside the chip".
BTW, prompted by your comments to Ignacio's answer, I'll add some extra points: semiconductors are called that way because the conductivity of the intrinsic crystals is intermediate between insulators and metals, but doped semiconductors can have very high conductivity (especially N-type ones).
As an example consider a power MOSFET in its ON state: it can reach a resistance between drain and source of few milliohm, just the kind of resistance level of a common relay's contacts, which are made of metal!
See, for instance, the datasheet of the IRF3709:
Moreover, free electrons are called that way because they are free as they are in a metal: they are in conduction band and that means that they can move freely across the entire crystal trellis, like in a metal. They are not bound to a specific atom.
