When importing there are fields that are required for the import to complete properly.
For Contact Import: First Name & Last Name are required. All other fields are optional. If you import the First & Last name a "Display Name" will be created by combining the two. If you want to import a Display name that would be different, such as including a middle initial or name in the display field, you should import the display name separately.
For Organizations: Organization Name is only require field
For Opportunities: Opportunity Name & Customer Name. For an Opportunity the Customer name will be either the Organization Name or the "Display Name" if the customer is a contact.
If you are importing Products (Sales & Business editions only) you will need to import the Product Name and the Product Category. Product Categories must be manually created through the U/I before performing the import.