The best way I've heard it describe relates to charge being a property of something. Electrical charge is one way of describing something. You could say that something is red if it appears red - you are describing the colour. You could also describe something as big if it is large - you are describing the size. If you describe the charge of something, you are describing how it relates to other objects.
Charge is an electrical property, which means that it is talking about electrons. In the same way that there are certain words you can use to describe colour, there are also certain words you can use to describe charge. These are positive and negative.
The phrase opposites attract is used a lot, and it ultimately comes from charge, because if two objects have an opposite charge (one is positive and the other is negative), they will attract each other. This is how magnets work - one has a positive end, the other has a negative end, and they attract each other and stick together.
This is the challenging thing to get your head round. Another way of thinking about it is like a Question and an Answer. You could have loads of questions kicking about, but they won't do each other any favours because they won't answer each other. Questions will really only be 'attracted' to answers. Similarly, loads of positive things won't help each other out, so they repel each other; and loads of negative objects will repel too. But put positive and negative together, and you get attraction.
I tend to think of charge as a bit like an invisible force that hangs around a particular object. You can't see if something is positive or negative - it's not like colour - but you can see the effect is has. If you have something which you know is charged, then you can hold something else to it; if this causes repulsion (pushing away) then it's the same charge; if it causes attraction it's a different charge; and if there is no attractive or repulsive force, then the second object has no charge.
We tend to talk about charges on atoms in terms of plus 1 or minus 1; minus 1 (-1) if it is negative, and plus 1 (+1) if it is positive. If it is even more positive, it may be plus 2 (+2) or plus 3 (+3), and the equivalent with negative. However, eventually things could end up being huge, which is why a measurement for charge was thought up: Coulombs. So in the same way that you could say something is big, or you could say exactly how big something is, you can also say that something is negative, or how negative it is.
Positive and negative, as discussed above, are charges - they are words that can be used to describe the charge of an object. They are complete opposites - if one thing is positive, it is completely the opposite to negative. But beyond that they're difficult to explain. Perhaps it would be easiest to explain how they come about.
As the section on the atom explains, atoms are made up of protons, neutrons and electrons. Two of these subatomic particles (i.e. parts of an atom) have a charge - a proton has a positive charge considered as plus 1, and an electron has a negative charge considered as minus 1. These don't relate precisely to the Coulomb values; it just makes things easier to work with. Neutrons don't have a charge - they are neutral.
Because protons would repel each other (they are all positive), think of neutrons as the glue that holds them together. Since positive and negative attract, the electrons are kept in orbit of the protons in the nucleus of the atom - that is, the electrons go round the bit in the middle in a circular shape.
The animation represents a carbon atom, with six protons and six neutrons in the middle, and six electrons around the outside. As with all atoms, carbon is overall neutral - the plus 6 from the protons is met by the minus six from the electrons: +6 - 6 = 0. Now, because the protons are in the middle, they can't move. However, the electrons around the edge are easily knocked around.
Look in the top right corner; there should only be one electron there. If an extra electron is attracted to the positive charge in the middle, then there are two in the top right corner, and seven electrons overall, but only six protons. +6 - 7 = -1. So the atom becomes negatively charged, with a charge of minus 1. The atom is now called an ion because it has a charge.
If the top right corner looses its electron, then there are a total of five electrons, but still six protons. 6 - 5 = 1. So the atom becomes a positively charged ion with a charge of plus 1. As with all things positive (including individual protons), this atom will be attracted to negative objects, and repelled by positive objects. The greater the charge (i.e. the higher the number after the '+' is), the greater the effect of it. So an ion with a charge of +8 will be repelled by another positive thing even more than an atom with a charge of +1. The equivalent is true for negative objects.
It's important to remember that charge always relates to the movement of electrons. Because protons are stuck in the middle, and weigh much more than electrons, they don't move from atom to atom. But electrons can move - this can be seen when you rub your hair against a balloon. Electrons are moved about, causing your hair to have a charge this is all the same, so your hair stands on end as it repels itself. Clever, hey?
Let's take something like water. Water has the chemical formula H2O - which means it has two hydrogen atoms in it, and one oxygen atom. The oxygen atom is described as electronegative, which basically means it's really good at attracting electrons. In fact, it will often try to grab them off something else, and in the case of water it does this - it takes the electrons from the hydrogen atoms (which are quite weak at keeping hold of their electrons).
It's not capable of completely robbing them, but because it does effectively 'look after them', the hydrogens have one less electron each - they are slightly positive. The oxygen, however, has extra electrons, so is slightly negative. Basically, overall, the water molecule is said to have polarity, because one side is positive and one side is negative.
That's all polarity is about - one side being positive, and one side being negative; and, obviously, it can happen easily as a result of electronegativity. It also has an interesting effect. Because opposites attract, the slightly negative oxygen from one water molecule will attract the slightly negative hydrogens from another water molecule. This leads to all the molecules lining up in the same direction!
Being terribly logical as scientists claim to be, something which has polarity is referred to as being polar - water being the prime example. Things which are not polar are called non-polar - this would be something which is all one charge, or more commonly something which has no charge at all. Something substances, such as ethanol, are partially non-polar, but do have some polarity. There's always an exception, hey?!
Polarity is a very important aspect of science, so it is well worth understanding! Unfortunately it's not always the easiest to follow. Simply understanding what positive and negative are is a challenge because you cannot see them, but once you've realised what's going on there, the polarity should follow logically.