Electrical – Electrical connection during car jump start

"Ground" is just a code word which, in this case, refers to the "current return common" circuit node. There is a complete circuit because everything electrical in the car, such as the starter motor, also connects to ground in order to return current to the minus terminal of the battery through the ground. The car's chassis is used for this return network, and so the entire chassis is an extension of the minus terminal of the battery.

During jump-starting, we connect the boosting battery to ground rather than to the dead battery's - terminal for the simple reason that this provides a more direct return path to the good battery which is powering the dead car: the return current does not have to travel through the dead battery's minus terminal hookup cable and then to the jumper cable, but can go directly from the chassis ground to the jumper cable.

A more direct return path allows for better current flow and less voltage drop, like plugging a big appliance directly into an outlet, rather than via an extension cord.

In case you're also wondering why the plus jumper connections are made first, then the minuses. This is because there is no harm done if you leave the minus jumper dangling in the chassis of the car. Anything it accidentally touches is likely to be ground. If you connect both alligator clips on one end before connecting the other end, the other end is now live and you can accidentally touch the clips together to create a short circuit. If you connect the minuses/grounds first and then go to connect one of the pluses, you can create a short circuit, because the opposite side plus is probably dangling and touching something that is grounded.

When the battery is supplying power (discharging) to, e.g., the starter motor, the direction of the electric current is out of the positive terminal through the load and into the negative terminal.

Within the wire and frame, the electric current is due to electron current which is in the opposite direction of the electric current.

Within the (lead-acid) battery, the electric current is primarily due to proton (hydrogen ion) current which is in the same direction as the electric current.

So, there are at least three currents to consider: the abstract electric current (flow of electric charge), the electron current (flow of electrons, a carrier of negative electric charge), and the proton current (flow of protons, a carrier of positive electric charge).

Note that when the battery is charging, the electric current is into the positive terminal and out of the negative terminal.