When a member logs in, a cookie is stored in his browser, so she doesn't need to log in again when she comes back the next day. The lifetime of this cookie decided when it will become invalid:
These settings are advanced settings. Normally, you shouldn't change them at all. In that case, cookie path is a simple slash ('/') and cookie domain is empty.
Normally, this should be set to 'no'. You should only set it to 'yes' when you have a HTTPS url and want cookies only to be sent over such a https connection.
You can setup Nucleus to store a cookie in which the time of the visitors last visit is stored. This can be used to put indications next to new items