The basic premise with electric fields is that opposite charges attract but like charges repel each other. The strength of these forces requires algebra in simple cases and advanced calculus and quantum mechanics in others. This is the basic force governing all chemical bonding, starting with attaching electrons to the nucleus of atoms to make any common atom in the first place. The nucleus having a positive charge due to the protons present will attract the negative electrons to just balance out the charge leaving a neutrally charged atom. The goal not only being to have the same amount of positive and negative charge but rather to get them as close as possible to each other.
Chemical bonding is a means to get the electrons closer on average to the nucleus of atoms being attached to each other to make up a molecule. There are different degrees of bonding strengths and even types. In living systems, the most common forms of atomic bonding are covalent and hydrogen bonds. Covalent bonds in a molecule are capable of making the molecule polar. This happens when the electrons are pulled in between two molecules so hard that the charge is no longer evenly spread out on the molecule leaving one or more areas with extra positive or negative charge. This leaves the molecule with at least one location with extra negative charge (from having an electron spending extra time there), and a location with extra positive charge (from having the regular electrons not spending enough time there). Water is a polar molecule and can be controlled to various extents in living cells based on these effects. Non-polar molecules include fats, lipids and waxes as examples of molecules which are not polar and so interact not through polar charges but through dispersion forces known as hydrogen bonding. This kind of bonding requires long chains of non-polar atoms in a molecule to overlap and only slightly redistribute the orbital electrons allowing the attraction to occur. These polar fields are extremely localized and generally are not largely effecting molecules other than those directly adjacent or very close to them. Non-polar bonding only takes place with direct contact.
Mixed types of bonding are also possible on the same molecule so that multiple forms of molecular binding can also take place. It is these processes which control proteins in cell walls that allows water, nutrients and ions in and out enabling cells to go through their life cycles. All of the processes are mediated by the electrical fields exerted between molecules and atoms in the organism.
The action of electrical current in most electronic devices is that of moving electrons through a conductive wire or possibly even a semiconducting device (like a transistor or computer chip). The process of an electrical current does require a circuit meaning that the flow of electrical charge has to occur in a closed loop. The circuit in portable electronic devices requires the use of a battery which has electrical current running through it but not in the same way that electrons travel through conducting wires. In the battery, positive ions move in the opposite direction of the external electrons in the circuit. These positive ions are simply atoms with one less electron in orbit than there are positive protons in their nucleus leaving the atom with a positive charge. In other words, this is a chemistry based electrical current. A positive charge moving to the left is electrically equivalent to a negative charge moving to the right and so this is the principle causing the equivalent current in a battery as exists in the external wiring to which it is connected.
This process of ion transport in a fluid (such as the gel or liquid in a battery) is how signals move from the brain to the neurons distributed throughout the whole body to activate muscles. It is literally electrical currents triggered in your brain that causes you to move and act although the current is like that in a battery (ion transport) rather than simple electron motion as found in conducting wires.
Electric fields of this kind control almost all organic chemistry, from simple combustion in burning oil and wood to the process of growing plants through photosynthesis. Just as it is needed in the oxidation of the food we eat to give us energy, electric fields play critical roles in geological, meteorological and even astrophysical effects as well. Material science, metallurgy, manufacturing and basically every form of engineering (except nuclear) are fundamentally founded in chemistry which is mediated almost exclusively through electrical fields.