Box 7 is used for Nonemployee Compensation. For example, if you're an independent contractor who does work for a company or individual, your reported income would appear here.
Box 3 is used for Other Income, IE, income that's not covered by the other elements on the form. For example, if you won a contest, had winnings from certain casinos, or received awards, the income would show up here.
Usually, these explanations are provided on the reverse side of the 1099-MISC form.