1.
If someone invades your personal space , they stand or lean too close to you, so that you feel uncomfortable.
N-UNCOUNT : oft poss N
2.
If you need your personal space , you need time on your own, with the freedom to do something that you want to do or to think about something.
Self-confidence means being relaxed enough to allow your lover their personal space.
N-UNCOUNT : oft poss N