I have a column used to insert dates for a certain activity. Is is possible
for me to restrict someone from entering a date that falls on a specific
day
of the week?

If we are talking about a user typing in a date, you could use Excel's
Data/Validation menu item to do that. For example, to restrict the user from
entering a date that falls on a Wednesday, you could select the entire
column and then use this Custom Formula in the Data/Validation dialog box...

=WEEKDAY(A1)<4

where I have assumed the dates are in Column A.

Rick