null=True sets NULL (versus NOT NULL) on the column in your DB. Blank values for Django field types such as DateTimeField or ForeignKey will be stored as NULL in the DB.
blank=True determines whether the field will be required in forms. This includes the admin and your own custom forms. If blank=True then the field will not be required, whereas if it's False the field cannot be blank.
The combo of the two is so frequent because typically if you're going to allow a field to be blank in your form, you're going to also need your database to allow NULL values for that field. The exception is CharFields and TextFields, which in Django are never saved as NULL. Blank values are stored in the DB as an empty string ('').
models.DateTimeField(blank=True) # raises IntegrityError if blank
models.DateTimeField(null=True) # NULL allowed, but must be filled out in a form
Obviously those two options don't make logical sense to use (though, there might be a use case for null=True, blank=False if you want a field to always be required in forms, but optional when dealing with an object through something like the shell.)
models.CharField(blank=True) # No problem, blank is stored as ''
models.CharField(null=True) # NULL allowed, but will never be set as NULL
CHAR and TEXT types are never saved as NULL by Django, so null=True is unnecessary. However, you can manually set one of these fields to None to force set it as NULL. If you have a scenario where that might be necessary, you should still include null=True.
IntegrityError is raised when Django attempts to save the record to the database. The field is not required to be filled in by the user, and that's the problem because at the database level it's not null.
In your explanation, models.DateTimeField(blank=True) you say that if this DateTimeField is left blank, an IntegrityError is raised. But I thought that blank=True means that the field doesn't have to be filled in by the user, so why the IntegrityError?
I think user798719 is referring to the value of blank, which should be False instead of True in your example: models.DateTimeField(blank=False) # raises IntegrityError if blank
No, Chris is trying to point out why having blank=True without having null=True would cause problems in a DateTimeField.
NOTE to Oracle users: It is not true that "CHAR and TEXT are NEVER saved as NULL by Django". It is true for most backends, but Oracle will force an empty string to NULL, so the Django Oracle backend is an exception to the above statement Django Docs
@ChrisPratt Minor correction to your post: CharFields can get saved as NULL in the database (translating to None in Python) if you set null=True. The docs even say to avoid setting null=True because it allows two different kinds of "blanky" values. I just tested this behaviour with Django 1.8/MySQL 5.6
Note that you may blank=True for a field entered by the system.