I know that the answer is yes. It is consumed, but in very little amount. My question is how it consumes electricity.
When the phone isn't connected the circuit is open at the phone end of cable, then how does electrons move around the circuit, because electricity is consumed when a circuit is completed and electrons can move around (I think so).
Yes, some electricity is consumed. A charger is a relatively complex device that has multiple "circuits" internally. Some of these circuits dissipate power regardless of whether anything is connected to the charger's output.
The amount of power is miniscule, however — on the order of tens to hundreds of milliwatts. You'd have to leave it plugged in for a year before it consumed a single kilowatt-hour of energy. In other words, each charger you have plugged in is adding about a penny to your monthly electric bill.
Because there are other components that use up energy. Timer circuits, any IC, the led, transformers, reference resistor dividers, etc. These are in parallel to the device to be charged. Multiple circuits are completed thus energy flows and is used. Look up quiescent current.
In any power supply, some current is consumed by the inefficiencies of the circuit, as leakage currents and as operating currents by the internal regulator circuitry.
But a mains charger is a switch-mode power supply (SMPS). Its regulator works by rectifying the mains then using a PWM-controlled switch to send that to a transformer going to the output. It only sends through the transformer the power the load requires, plus a little extra for what's lost by its own inefficiency. To stay in regulation with no load, the circuit contains a minimum load within itself and this uses a small amount of power. You can find plenty about SMPS their internal design and operation on the internet (search for 'smps basic operation').
No component is ideal, capacitors leak, transformers require magnetising currents. Control/regulation circuits require power to operate. So there are many ways current can flow other than into the load.
On a modern charger based on a rectifier followed by a flyback converter no-load losses are generally very low. Under light or no load the flyback converter will switched to a discontinuous mode with very short bursts of operation to make up for the small amount of energy lost to leakages and powering the controller.
OTOH on an old-fashioned charger that has a mains-frequency transformer there are significant no-load losses. A noticeable amount of magnetising current is needed by the transformer core and this current leads to resistive losses in the transformer windings.
If the phone was connected directly to mains then no, it would not use power while disconnected. However, mobile phones (for example) are NEVER connected directly to mains. Instead, they are connected to a step-down circuit that steps down mains voltage (120VAC or 240VAC depending on what country you live in) to usually around 5VDC. This can be done in various ways, but the two most common methods for chargers are step-down transformers and buck converters.
Transformers consist of two windings around an iron core. One winding (with more turns) is connected across mains, and the other winding (with fewer turns) is connected to a rectifier, filter capacitor, and then to the phone. Even when the phone is not connected, current is still flowing through the primary winding (the one with more turns connected across the mains plug) and thus power is dissipated.
Buck converters are a type of switching supply that turns on for a short period of time and turns off for a longer period of time. This happens tens or hundreds of thousands of time per second. The ratio of the on-time to the off-time determines the average voltage, which is passed to the output. However, this circuitry runs and draws current even when the output is not connected to the phone, so it too dissipates power.
If there is a closed loop across the mains, there will be current draw and power dissipation. In the case of transformers and switching supplies, there are closed loops in both cases, so the charger will use power even if the phone is not connected to it.
