One thing that electrical appliances have in common is that they, of course, run on electricity. Another is that they take the electricity and convert it into some other useful form of energy. The majority of electrical appliances accomplish this by using an electric motor. An electric motor is a device that receives electrical current coming into it and, through an arrangement of wire windings and magnets and a rotating shaft, converts the electrical energy into rotational energy that can do mechanical work.
Depending on the function of the appliance, different things can be attached to the motor's shaft. For example, in the case of a food processor or blender, it's a set of blades of various kinds that chop food. A mixer is a similar appliance that works in a very similar way to a food processor or blender. One difference is that perhaps the RPMs (the motor's revolutions per minute) are lower, since a mixer doesn't have to do the job of cutting and chopping.
A vacuum cleaner is another example of an electrical appliance. It also has a motor that takes electrical energy and converts it into mechanical energy. But in the case of a vacuum cleaner, a rotating device causes a current of air that creates suction. A vacuum cleaner must have an air intake and an air outlet. In between the air intake and the air outlet is a filter or a system of filters to trap foreign objects and particles in the air stream. Modern and more sophisticated vacuum cleaners have highly refined filters, often a combination of more than one type of filter, that remove extremely small particles from the air.
We may think of electrical appliances as being those items used inside the home, but in the broadest sense they include outdoor equipment, as well as indoor. In this sense, electrical appliances include such items as hedge trimmers, weed trimmers, electric chainsaws and leaf blowers. Again, the one thing they have in common is an electric motor with a shaft attached to a device that does the work for which the appliance is specialized.
We can also include in the list cordless items that run on rechargeable batteries. Such things as cordless drills and cordless weed trimmers running on rechargeable batteries would fit in this category. Their internal workings including a motor running on electricity and a rotating shaft to do the work, just as in a device that plugs into a wall socket. The form of electricity in a cordless appliance is what's called DC, or direct current, versus AC, or alternating current (the typical wall outlet). But once the electricity is supplied to the motor, the way the device works is the same.
A generator is essentially the reverse of an electric motor. In an electric motor, electricity is the input, and rotational energy and mechanical work are the outputs. In the case of a generator, some other energy source besides electricity causes the rotation, and electrical energy is the product or the output. An electric current is the result of causing the generator shaft to turn. In gas-powered generators, a gasoline engine makes the shaft turn. Generators can also be small and can be turned by hand or attached to a bicycle or any other means of a crank that will turn the generator shaft. A small windmill for domestic use, in the broadest sense, is an example of an electrical appliance. Instead of a motor, it features a generator.
The range of items that qualify as electrical appliances is broad. There are more examples than those mentioned here. But the one feature most of them have in common is that they receive electrical energy and convert it into mechanical work. In the majority of appliances, this job is done by an electric motor. An electrical generator is the exception to the rule since it does the opposite, taking the input of some other energy source and converting it to electricity.