Electric charge is a fundamental property of matter. Matter that possesses a charge is influenced by, and produces, electromagnetic fields. The interaction between charge and an electromagnetic field is the source for one of the four fundamental forces.
Charge was discovered by the Greeks when they would rub firs on various substances, such as amber, and build up a static electric charge. The greeks noted that the charged rods of amber could attract light objects, like hair. The greeks also noted that if they rubbed the rods long enough, they could even get a spark to jump.
Jump to 17XX, and the study of electricity is all the rage. One of the foremost experts is a man named Benjamin Franklin. Franklin imagined electricity as being the flow of a fluid that he called charge. He posited that rubbing amber rods caused this charge to flow. He also posited that all matter had this fluid within it, and when it had too little charge it was negatively charged, and when it had an excess it was positively charged. So, Franklin arbitrarily picked the direction in which positive charge flowed when a fur was rubbed on an amber rod (not sure about this, does anyone know how he actually decided?). Unfortuneately for us, he had a 50% chance of guessing right and he got it wrong. Franklin didn't know that, as later scientists discovered, that there were actually two types of charges, and that the charge he identified as positive doesn't actually flow in most cases.
In modern physics, there are two types of charge: positive and negative. Negative charge is carried by a subatomic particle called the electron (wasn't electron greek for amber, and that's where the name comes from?), and positive charge is carried by the (?) quark. (?) quarks aren't usually found interacting directly with electrons, however, because they are usually held inside of a larger subatomic particle called the proton. Electrons and protons have equal charges, but of opposite type.
Aside from the properties described in articles about electromagnetism, it is worth noting that charge is a relativistic invariant. What this means is that any particle that has charge q, no matter how fast it goes, always has charge q. This property has been experimentally verified by comparing the charge of a helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at increadible speeds) is the same as two duterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus).