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Why does the electric charge flow?

Dear student,
Electrons are negatively charged and they are mainly responsible for the flow of current in the conductors.
So when  we connect both ends of a conducting wire with battery; it generates a electric field across the wire. Now as free electrons are negative they flow towards the positive terminal of the battery and as a consequence current flows in opposite direction within the wire.
Similarly, for semiconductors, charges responsible for current conduction are positively charged hole (having charge of +1.6 x10-19 C) and negatively charged electrons. In this case holes flows towards the -ve terminal of the battery whereas electrons moves towards the +ve terminal of the battery.
So the electric potential diffrenece across the wire is mainly responsible for the flow of electric charges.

Regards,

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Electric current or electric charges flow because of the Coulomb's force on them . The force is due to electric field. The field is created because of potential difference between two end points of a conductor.The potential difference occurs due to improper charge distributions or due to accumulation / concentration of charges.Because battery has charges accumulated on its terminals, current flows when the terminals are connected in a circuit.
Hope This Helps You :)
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The particles that carry charge through wires in a circuit are mobile electrons. The electric field direction within a circuit is by definition the direction that positive test charges are pushed.
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Dear student,

Electric charges flows into the wire because when the two ends of the wire is connected to the battery then the battery generates an electric field in the wire. This electric field forces the free electrons (that the metal wire consists) to move toward the high potential (positive terminal) of the battery.

Regards
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Because of the difference in potential at two different points. So to balance electric potential at both points charge flows. Just like water flows from a tank containing more water to a tank containing less water connected through a pipe till the water level is same in both tanks.
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