Simply put, a file is a collection of bytes stored together. An example of a file could be a Text File (a collection of alphanumeric characters that, when put together, form a readable document) or a Bitmap Image File (a collection of bytes that software would then interpret as elements of an image).
A database is a special type of file that holds many tables. Each table can hold many fields as well as records. Think of a table as a spreadsheet. Each column represents different fields, such as "UserID", "LastName", and "CityOfResidence". Each row represents a record, or an entry, in the table, such as an entry for John Smith who lives in Albuquerque.
An example of a database would be one that has three tables: Books, Instructors, and Courses. Different fields in the "Books" table would be "Author", "Publisher", "Title", and "ISBN". Different records within "Books" would be, for example, an entry for "Learning Java in 20 Days" (Title) by John C. Doe (Author), published by ABC Publishing Co. (Publisher).
Each table in a database requires one field to be designated as the Primary Key. This means that, in order to uniquely identify a record in a table, one field needs to be used. In a "Students" table, the "StudentID" could be used as the Primary Key, since no two records (students) can have the same Student ID. For "Books" it could be "ISBN", since that is unique per book title.