The number entered here determines how many "upload boxes" are shown when the student submits a piece of work. The number can be zero, that is no attachments are allowed. If attachments are expected, the number is set to 1, 2, up to 5. Normally the number will be 0 or 1, but in some assignments the students may be asked to submit more than one attachment.
If the number is set to 3, say, and the student only attaches two files to their submission, the two files are attached and there is no warning message. Thus, when submitting work (in a single operation) students can attach an arbitrary number of files to their submissions, up to the maximum number given by this option.
Note this option does not set the maximum number of attachments a student can add to their submission. It just determines how many "upload boxes" are shown. The student is free to add more attachments to their submission by editing that submission. This would be unusual.
The default value for this option is zero, that is no attachments are required.