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It means that she feels you are not respecting that she needs time and space from the relationship which means that she doesn't want any contact while she is deciding what she wants and she may feel that you are invading that privacy that she wants and not respecting that she wants space to think about things and what she wants to do next about the relationship or friendship. If you want to have any kind of relationship with her it's best to respect what she has asked of you even if you want to contact her don't she will respect that you gave her that space and will consider you as a friend or even consider giving the relationship another chance but you have to be careful not to over step the boundaries that she has set because you are broken up.
If it's new from the break up then she may feel uncomfortable talking to you about family problems and things that you talked about when you were together what you are going to have to do is give her the time she wants so that she doesn't feel like you are trying to be back at that place when you were together. After the breaks up she wanted to take a break from you simply because she felt she needs some space from the relationship.
While this indeed may be true and you giving her space is already the best thing for you to do. Waiting on her to come back or invading her space before she is ready is one of the worse things you can do. She needs space because the relationship with you has grown to its peak and she may feel as if she can't grow into the person that she wants to be as long as she is in a relationship with you.
As long as you wait for her to get the space she needs in order to come back you aren't growing. She may not ever come back to the relationship that you may be waiting for if you haven't grown yourself. You must continue to grow in your own self improvement and goals in life just like she is attempting to do in order to get her back. While it would be nice if you could wait for her and grow at the same time it simply is not possible, the time apart will make you both stronger and help you to learn from your mistakes. The longer you wait the more growing she will do and the more you will have to grow in order to get her back; which isn't going to happen as long as you are waiting. If you show her that you are willing to give her that time and also work on the things that made you break up in the first place it will give you a better chance of winning her back but as long as she sees that you are not changing but staying the same she will always want that space.