I know this isn't the right place for asking this question, but in other places the answers are so awfull.. I'm studying eletricity, so, I start seeing things like "charges", "electrons has negative charges",etc. But I didn't quite understand what charge is. I search a little bit on the internet and found it related to electromagnetic fields, then I thought "negative and positive may be associeted with the behaviour of the particle in the field, great!", but the articles about e.m. fields already presuppose "negative" and "positive" charges. In other places, I see answers relating charges to the amount of electrons/protons in an atom, but if that's right, the "negative" electron is an atom without any protons? What about the neutron? So, my questions are (1) What are charges; and (2) How a particle can "be" electrically charged. What does that really mean? Thanks for your time.
I would say that charge is a theoretical prescription describing a way of how a particle interacts with electromagnetic field. Since we are talking about a theory that should describe and predict various phenomena, we need to start with definition of fundamental object.
If we are talking about Newtonian mechanics we face phenomena related to interactions of particles with each other by a direct mechanical contact. We characterize these interactions by force, momentum, etc. Fundamental characteristics of a body will be the mass. Theoretically, you may consider objects of positive, negative or zero mass in mechanics. However, from experiment we know, that there are no objects with negative mass.
The same is true for electrodynamics, where we see objects interacting through a field. Now to describe the ability of an object to generate or to fill this field, we introduce the charge. So, as was already said by zeal charge is just a property of an object, same as mass.
Concerning your second question. Firstly, one should note that any object may have any charge irrespective of electrons. However, we know that atom is a complex object composed from electrons, protons and neutrons. Hence, in order to figure out charge of an atom we should assign some charges to its fundamental constituents.
From experiments we know that electrons, neutrons and protons interact with each other and with electromagnetic field in such a way, that we may define $q_e=-1$, $q_p=+1$, $q_n=0$. Now, just by summing charges of constituents of a complex object we can derive its charge.
Hence, in brief: charge is such theoretical prescription in electrodynamics, that allows to predict electromagnetic phenomena.
If you're looking for a definition of charge, then I can't give you any more than this.
Charge is the property of matter to interact with electromagnetic field, analogous to masses in gravitational field (but, much more stronger!).
If you're looking for a way to visualize, then there's no way. I should begin with the statement that answers to these questions can turn out to be philosophical.
Because, there's no convincing definition for these things. We can only know/talk about the characteristics of such a thing, because all we know (based on observation) is that when we account for something like the charge, we can explain some of the phenomena happening in nature.
Properties like temperature, mass, etc. are easily conceivable because we have a number of ways to have a "feel" about them, like heat for temperature, and weight (more specifically, the gravitational field) for mass.
If there isn't a way to visualize, then there's no way you can be convinced, except believe that something like that really exists. Languages also, are of this kind. For instance, I could ask you to define a cat. You'll start describing it as, four-legged mammal, has no ability to roar, etc. What you're doing is, use a few base words to describe a particular word, based on your observation of the animal. Or, we could extend this even further, to alphabets. Do we have a definition for "A"?
My point is that we need a few base items to describe the phenomena happening in the outside world. And, charge is one among them!
Ans 1: Charge is the physical observable corresponding to a conservation of a certain symmetry.
Ans 2: The electric charge or Electromagnetic charge is due to the electromagnetic U(1) gauge symmetry.
See also this post: Is there any theory for origination of charge?
Charge is a physical property of matter. Since, in experiments of rubbing dissimilar things like rubbing glass with silk etc, and other detailed study of this property, it is observed that objects possess this property by which they experience attraction and repulsion. This led people to realise that there are two opposite form of it so the names given as positive charge and negative charge.
A point charge doesn't really exist. It is hypothetical. An electron is not a point charge. An electron is a particle that posses this property and experiments show that it possess the negative charge.
A point charge is an idealisation to study how charged objects affect other charged or neutral objects.
So a surface of a body is positively charged doesn't really mean that positive point charges are spread on it but it is rather like a "continuous fluid" of that positive property is uniformly spread on it.
It is this property of matter which is responsible for interaction with electromagnetic field. Its the charge that interacts with electromagnetic field as mass with gravitational field.