I have a basic question about electronic ground. For example, if electrons travel from the DC battery's negative terminal through the conductive wire to the positive terminal of a DC battery with a LED as a load, how would adding ground symbol in a schematic circuit between the conductive wire of the negative terminal connecting to the LED change anything in the current flow?
In many (most?) circuits, the ground symbol simply indicates the point in the circuit that we will call "zero volts" - where we will place the black meter lead when measuring voltages elsewhere in the circuit.
In many circuits, this "zero volt" point is the most negative terminal of the power supply, but it could, if the designer desires, be the most positive terminal of the power supply. In many analog and op-amp based circuits, this "ground/zero volts" will be the mid-point of the power supply, so we have both positive and negative voltages in the circuit.
In AC power distribution systems, and in some radio antenna systems, "ground" really does indicate a connection to the earth, eg. a metal spike actually stuck in the ground.
Beware of the word "ground," since it has several conflicting definitions. The experts may be able to figure it out from syntax, but for everyone else, we can avoid much confusion by avoiding the word "ground." Use less general terms instead.
For example, "ground" can mean one or more of the following, or even a mixture of several:
"Ground" can be a common connection for multiple power supplies, but not connected to the earth. The chassis of a car is one example, and while most manufacturers connect their chassis to the battery negative terminal, older Volkswagens connected theirs to the battery positive. "Ground loops" refer to this definition.
"Ground" can mean an arbitrary reference point in a circuit, "schematic ground" or a point used to define the voltage-drops throughout the device.
"Ground" can mean the inside of a shielded enclosure, including any shield-planes built into a pc board. In many amplifiers, the metal box is the system ground. In high speed circuitry we'll find separate "logic ground" and "analog ground," each connected to separate conductors used as shields.
"Ground" can mean an RF counterpoise: a connection to a large conductive object. In portable receiver front ends, a short wire is one "antenna" terminal, while the other terminal connects to the rest of the circuit as a "ground."
"Ground" can mean "the opposite of electrically floating."
"Ground" can mean "Earth connection," a terminal with an actual metal stake pounded into the dirt. Earth connections are important with lightning hazards and AC line safety, with AM and shortwave antennas, PA sound systems in wet outdoor environments, high-voltage electrostatic build up and ESD/EMP problems.