What does it mean if I have slightly brown discharge instead of an period and it lasts for about a week?

It could mean that you are taking your birth control pill wrong, it could mean that you are still very young and your hormones have not adjusted, it could mean that you are going into menopause.

See, there are too many variables here to know for sure. You need to provide as much info as possible to get an answer suited more for your particular situation.