To keep it simple for now (once you get to college physics this will be expanded), charge is electrons piled up, or lack of electrons where you'd expect there to be some. Electrons have negative charge and protons positive charge. A normal atom has the same number of electrons as protons, so no net charge.
On some atoms, the outer few electrons are somewhat "loose". When you have a whole bunch of these atoms all next to each other, like copper atoms in a copper wire, these loose electrons can jump around between adjacent atoms. However, if they jump too far, they leave a positive charge (since a negative one went away) where they left, and a negative charge where they are. This imbalance of charges creates a electric field, which you can think of as a force field that pushes and pulls on electrons. Electrons are pulled toward to positive charges and pushed away by negative ones. This electric field therefore won't let the electrons vacate one location and pile up in another over the space of a few atoms.
A voltage source, like a battery, is something that creates a electric field. If you connect opposite ends of the battery to opposite ends of this copper wire with all the somewhat mobile electrons in it, you can get all the electrons on average to move from the negative voltage end of the wire to the positive voltage end. To keep maintaining the electric field applied to the wire, the battery then pumps the electrons that flow off the + end of the wire back onto the - end of the wire, where they again hop between copper atoms and end up at the + end again.
The mass movement of electrons is called current, which is charges flowing. This is a lot like current in a river is lots of little water molecules flowing. Since the charge of one electron is very very tiny and of little use at our human scale, we use a unit of charge called the Coulomb. However, a Coulomb is just a calibrated pile of charge. In fact, it's about 6.24 x 1018 electron charges worth. Actually it's -6.24 x 1018 electrons since we arbitrarily decided electrons have negative charge.
Again to keep the range of numbers nicer on a human scale, we measure current in Amperes, which is one Coulomb of charge flowing by every second. So if you have 1 Ampere (sometimes "Amp" or the official abbreviation "A") flowing left to right in a wire, then there are actually 6,240,000,000,000,000,000 electrons flowing right to left per second past any one point along that wire.
Now that you have a basic idea what charge and current are, forget about electrons moving with their negative charges. The rest of electronics is all built on Amp and Coulombs. Think of that as the conceptual units of current and charge you'll be using from here on. The fact that these happen to (usually) be based on actual negative charges is irrelevant and just invites confusion.
So now let's go back to that battery that caused current in our wire. A battery is really just a pump for charge. In other words, it can make current. However, there is one more metric that is important to mention here, which is how hard the battery can push. One battery may be able to push harder on charges than another, just like one water pump can make a higher pressure than another. It is this pressure that makes the electric field that makes charges move, which is current. This electric pressure is measured in units of Volts. The more Volts a battery can make, the more current it can cause to flow thru the same resistance. This is just like a higher pressure water pump can make more water flow thru the same size nozzle.
So how can we related voltage, current, and resistance? As you can probably see more voltage (pressure) makes more current (flow), but more resistance (smaller nozzle) makes less flow. To put this mathematically:
current = voltage / resistance
This also gives us a definition of resistance by rearranging this equation:
resistance = voltage / current
The concept of resistance comes up a lot in electronics, so we have a special unit just for measuring it, called the Ohm. In fact, the Ohm is defined as:
Ohm = Volt / Ampere
We have short abbreviations for all three of these quantities since just about all of electronics is based on them. A Volt is abbreviated "V", the Ampere as "A", and the Ohm with the greek letter "Ω".
This equation that relates resistance, voltage, and current is a cornerstone of electronics, and is called Ohm's Law, after the guy who first came up with it.
Let's go back to the first form of Ohm's law I showed, which tells us how much current we get:
In physical quantities: current = voltage / resitance
In common units: Amps = Volts / Ohms, or A = V/Ω
That's a great deal to think about already. Try to wrap your mind around this before going any further. Ask questions here as you need to to understand this. Once you get this, we can go on to all kinds of cool stuff.