Hi Tony The answer lies in the electrical panel. Most panels have two very large wires that come into it from the electic meter (usually outside), with each wire in the electric panel attaching to what is called a buss or a heavy metal bar (two of them) in the panel. Each buss is 120 volts, but the alternating current going to each is 180 degrees out of phase with the other. From the peak of one cycle (+120 volts) to the trough of the second cycle (-120 volts) gives you 240 volts. Assuming you have a breaker panel (not screw in fuses), the 220 volt breakers will attach to both busses, whereas 120 volt breakers will attach to only one side (one buss). Your electric dryer will require its own 220 volt breaker, so you must have space on the panel for this. The washer reqires only a 15 amp, 120 volt line that can be taken from an existing electrical circuit already in place.
If you are still not clear on this, might want to have a local electrician take a look.