Electrical Current
Achieving Balance
Atoms want to be balanced; that is, if they are positively charged (have too few electrons), they exert an attractive force to try and take free electrons to achieve balance; a neutral charge. Atoms that have a negative charge (too many electrons), tend to want to get rid of excess electrons.
Usually, electrons jump from negatively charged atoms to positively charged locations. We can think of this as an electron filling a "hole." When an electron moves in this direction, it leaves a hole behind it, which has a positive charge. So, we can think of electrons flowing one way and holes (or positive charges) flowing the other way.
This movement of electrons and holes is what we call electrical current.
Hole flow was first observed and measured in the 1740s by Benjamin Franklin, who also named the charges as positive and negative. Benjamin Franklin's work kickstarted the practical use of electricity, and a big part of electrical theory and electrical engineering were based on it.
Many diagrams like the following use the hole-flow convention. These diagrams are a bit misleading because they imply electrons flowing from a positive charge to a negative charge:
It wasn't until 150 years later, in 1897, that Sir J. J. Thomson posited that atoms were made of electrons and discovered that electrons, rather than holes, were thing that was actually moving.
However, in practical usage, it doesn't matter, because most everything has standardized on Benjamin Franklin's convention. For this reason, many people use the term charge carrier, which can mean either a positive charge (hole) or a negative charge (electron).
Speed of Electrical Current
We think of electricity as moving at near the speed of light, which is how we can communicate around the world on the phone or via the internet almost instantly. But electrons actually flow, or drift as physicists say, pretty slowly. So how is this possible?
Well, it turns out, what actually moves is the electromagnetic wave, which is the propagation of the charge moving. Consider a hypothetical tube full of marbles:
If you add a marble in one end, a marble will fall out of the other end almost immediately, even though each marble only moved a small amount:
Now imagine that those marbles are electrons; the effect of adding an electron is near instantaneous, or as fast as anything can travel; the speed of light. In a conductive material, electricity works the exact same way, even if it's a very long wire. So, the data that's encoded in the patterns of electrons on a wire when a phone call is made around the world may travel only a short distance, but on the other end, the effect is the exact same as if those electrons traveled the whole way.