What is meant by the slogan personal is political?

What this
slogan means, in its most common usage, is that there is no real difference between womens
political issues and their personal issues.  It was used to argue that issues that people
denigrated as personal issues that women should take care of on a personal level were really
political issues that should be dealt with as a society.

In the late 1960s
and early 1970s, many womens issues were not taken very seriously by many people.  When women
wanted, for example, more help from men in terms of childcare and housework, it was seen as a
personal issue.  When women talked about the pressure that society put on them to be attractive
and about the problems that caused with things like body image, the issues were dismissed as
personal issues that women should deal with on their own.

The personal is
political was used as a slogan to argue that all of these were truly political issues.  It meant
that all of these issues came about because of overall societal factors.  When women wanted more
help from men, it was an issue of society-wide attitudes about what constituted mens work and
womens work.  When they worried about body image, it was because of issues about how society
portrays women and about what factors cause women to be valued or not valued. 

Thus, the slogan was meant as a way of arguing that womens issues should be taken more
seriously on a political and social level.