I'm not a scientist, but I play one on tv. Can anyone explain in simple, easy to understand terms?
Electrical current is the movement of electrons, which have negative charge, through a conducting medium, like a wire. So hook up a battery to a circuit with a light bulb, like we all did in science class, and electrons flow from the negative post of the battery, through the circuit, to the positive post.
A couple hundred years ago, there was a notion of positive and negative charge, and that when there was a difference in charge, current would flow until the difference was resolved. For instance, you could rub a piece of silk on a glass rod, and charge would be exchanged between them, one would be positively charged, and the other negatively charged.
But there was no notion of electrons, and no way to determine whether it was the negative charge moving in one direction, or the positive charge moving in the opposite direction, or if they both just moved in opposite directions. Ben Franklin took a guess, and established a convention that would be consistent with positive charge moving through a circuit.
That convention continues today. When Electrical Engineering students take their first circuits course, they're taught a convention in which the direction of current flow is from, for instance, the positive post of a battery, through the circuit, to the negative post, a convention which assumes that it is the positive charge that moves. All calculations are done from that perspective. Once you know about electrons, it seems unintuitive, because it's really more correct to think of the negatively charged electrons flowing from the battery's negative post, through the circuit, to the battery's positive post.
But, ultimately, whether you have negative charge moving from right to left, or positive charge moving from left to right, it doesn't really matter when it comes to solving circuit equations.
You can compare this to questions like "does heat move from hot to cold, or does cold move from cold to hot?" or "does light move from brightness to darkness, or does dark move from darkness to brightness?" You may have an intuitive notion of what the thing is that moves, but from a mathematical perspective, it may not make significant difference, because each "thing" can be defined as the absence of the other thing.
-harry