To me this old saying means that you don't get to redo your first impression to someone.
Explanation:
For example, if you are nice to someone the first time you meet them then they will know you are a generally nice person who is in a good mood. But, if you are rude, snobby, or tell someone off when you first meet them then they will think you are a bad person and won't want to be around you.
The primary message that Congresswoman Chisholm tried to convey is that we are all equal, both men and women, both African-Americans and Caucasians. Regardless of our sex, gender, and skin color, we are all equal.