The thing to remember about electrons is they are a negative charge. That means that the direction of current flow of the charge (currentpositive charge) is opposite to the direction of flow of the actual electrons (negative charge). Picture it like those "compression jams" you get on the motorway (freeway) where cars that are travelling too close together have to slam their breaks on to avoid running into each other. The one at the front slams its breaks on briefly then carries on. The one behind has to do the same, and so on and so forth. You then get a wave effect travelling in the opposite direction to the direction of travel of cars as they slam their breaks on in turn. The cars are moving forwards, but the compression jam is moving backwards. Similar in a circuit - the electrons are moving forward, but the charge is moving backwards.
Another way to visualize it is as a bubble in a pipe of stationary water. The bubble moves in one direction, but in order for it to do that the water has to flow past the bubble in the opposite direction.*
So the chargecurrent flows out of pin 13 through the LED and to ground, but the electrons themselves are actually flowing from ground through the LED and in to pin 13 (where they eventually return back to ground through the power supply).
That said, normally the blue (or black) marked line of holes down each side is used for ground, and the red line of holes is used for power. As both sides of the board are separate it is possible to use different voltages on each side, or the same voltage on both sides, etc. That can be especially useful when you're working on a circuit that has, say, +3.3V and +5V in it. Another common split usage is for a positive voltage on one side and a negative voltage on the other - common when working with op-amps. Just remember which is which.
* This is a complete lie, but it's as close as you need to know at this point in your education. https://en.wikipedia.org/wiki/Lie-to-children



