It means the week containing the fourth day of whichever month is being discussed. Commonly, weeks are identified by the Monday date. Example: (person calling for a car service appointment) (ring...) "Hello, XYZ auto service. How can I help you?" "I would like to bring my car in for an annual safety inspection." "hmmm... The week of Monday, March 1 is completely full. We have plenty of openings the week of the 8th. Do you have a preferred day?" ... (and the conversation continues to set a date and a time)

the week of the fourth of July