Why do some members have status "Approve" in the Manage screen?

These are members who have self-registered online. As the Community Manager, you can check their registration details and decide whether they should be given access to the community. 

Once you approve them , they will be notified automatically by email that they are allowed in. 

The Manage screen will also record who approved them, and when -- handy if there is more than one Community Manager. 

Also if another member of the community happens to invite them to join after they have already registered, this acts as an approval. The inviting person's name is recorded so you always know who let them in. Nice.