A domestic corporation is one formed in the state in which it is doing business. A foreign corporation is one incorporated in another state or country and does business across state lines. The process of setting up a company in a foreign state is called foreign qualification.
Many people choose to incorporate in their home state. However, if your corporation will not "do business" in the home state, it may be wise to incorporate elsewhere. "Doing business" usually means more than just selling products or making passive investments in that state. It usually requires occupying an office or otherwise having an active business presence.
In the past, there was some advantage to incorporating in Delaware, since that state had very liberal laws regarding corporations. Many national corporations are incorporated there. However, in recent years, most states have liberalized their corporation laws—so today, there is no advantage to incorporating in Delaware for most people.
Nevada has liberalized its corporation laws recently to attract businesses. It has other rules that allow more privacy to corporate participants. It also does not share information with the Internal Revenue Service and does not have a state income tax.
If you form a corporation in a state other than the one in which your business is located, you will be required to have an agent or an office in that state, and you will have to register as a foreign corporation doing business in your state. This is more expensive and more complicated than incorporating in your own state. Also, if you are sued by someone who is not in your state, he or she can sue you in the state in which you are incorporated, which would probably be more expensive for you than a suit filed in your local court. In some states, your corporation may be required to pay state income tax.