Can we treat superpostion principle of charges as a simple vector addition? In my physics NCERT class 12 it says that:

Superposition principle should not be regarded as obvious or equated with the law of addition of vectors. It says two things: force on one charge due to another charge is unaffected by the presence of other charges and there are no additional three-body, four-body etc. forces which arise only when there are more than two charges."



*

*I always think superposition of charges (and forces) to be very obvious and unimportant. Why is it so not obvious vector addition?

*What is the meaning of last line (the bold italic one)?

 A: Superposition of charges (or the electric field etc) is a physical assumption, not a mathematical one. You could imagine that there is an interaction between electric fields such that if two fields "overlap" then other things happen (like stronger fields, perhaps). For example, there wouldn't be anything mathematically incorrect with saying that the new field due to two fields is given by
$$\mathbf E_{1+2}=k(E_1+E_2)^3\cdot\frac{\mathbf E_1+\mathbf E_2}{|\mathbf E_1+\mathbf E_2|}$$
for some constant $k$ to make the unts work out. However, we don't see this type of thing. It does seem like electric fields do just linearly superimpose (however, their energies do not).
The bold part just says that this type of thing doesn't happen for when there are $N$ or more fields present, i.e. they are just being more general than the case of just two fields. It would also be mathematically valid to say that at some point linear superposition no longer holds, so they need to cover everything in the statement.
A: Superposition principle is:

Force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to the other charges, taken one at a time. The individual charges are unaffected due to the presence of other charges. 

We use vectors because they are convenient in applying Coulomb's law. While Coulomb's law states the electric force between 2 charged particles, it seems obvious to use vectors. But, a vector has an algebraic structure. This is independent from the fact that Coulomb's law describes a force. So superposition is not necessarily obvious.
Three body forces:
In nuclear physics, it is not possible to rule out completely three body and higher particle-rank terms in the nuclear interaction. A three body force is one which is felt only when there are at least three particles present, for example, in a three-nucleon system such as a triton, the nucleus of tritium, or a He-3, made of two protons and one neutron, a two-body force acts between nucleons 1 and 2, between nucleons 2 and 3, and between nucleons 3 and 1. 
If, after taking away the sum of interactions between these pairs, there is still a residual force left in the system, we can then say that there is a three body force between nucleons.
All the available evidence indicates that such a term, if present, must be very much weaker than a two body force. Now, think in similar terms about four body forces. It is a field of research currently, and not much is known about the presence of three body forces with the possible exception of three-nucleon systems.
It was written in the book to mandate the fact that superposition principle operates in the absence of such fields, and that it cannot be used to analyze such systems.
References:
Introductory Nuclear Physics by Samuel S.M. Wong, Second Edition, Wiley-VCH
A: I would like to quote a footer here from DJ Griffiths, Introduction to Electrodynamics.

The principle of superposition may seem "obvious" to you, but it did not have to be simple: if the electromagnetic force were proportional to the square the total charge, for instance, the principle of superposition would not hold, since $(q_1+q_2)^2\ne q_1^2+q_2^2$ (there would be "cross terms" to consider). Superposition is not a logical necessity but an experimental fact.

Explanation: In reality, $F = \frac{kq}{r^2}\hat r$ (units compromised) on a unit test charge far off as compared to the collection of charges in consideration. If the force expression were $F = \frac{kq^2}{r^2}$ experimentally, the presence of another charge(s) would have affected the force due to one charge at consideration, which is not the case, hence the superposition principle.
