What does it mean if a female starts bleeding a week after her period. please am worried and concerned this hasn't happened before?

Not uncommon: By the time you are 32 it will have happened more than once. Multiple normal things can cause this, like not having fully sloughed off your endometrial lining during your usual period, stress and hormonal changes, change in bcp to name a few. If it stops in a few days, no worries. If it persists more than 10 days, discuss with your gyn doc.