Installing and upgrading help

If they are in the database then they have been approved. The longer they have been in the database and the more times they have been downloaded then the more people have explored the features.

It depends what you hope "approved" means. They have passed certain quality control checks in order to be included in the plugins database. I think it would be incautious to say more than that. 

In particular, try to establish if plenty of people are actually using the plugin and consider what will happen if the developer goes away to do something else and it ceases to be developed/supported.