Think about the literal meaning first :
seek = look for, search for, find
path = a route that leads from A to B and can be followed in order to arrive at B - ie a destination
So what Mary is saying is that, as she is now an adult, she must make her own decisions about what to do with her life - independently of the wishes of others (her family, presumably her parents). So she is telling her family to move away and leave her to live her own life without them.
She is using the expression metaphorically - but the metaphor of "following your own path in life" is very common.
This article, for instance, uses it repeatedly.