As a Noun:
1. A person who is inquisitive and always wants to know everything that is happening. Informal Australian English = sticky-beak.
2. The desire that someone has to know about things and to learn as much as possible about them. English = curiosity.
As a Verb or Adjective:
1. To try to find out about things that do not concern you. English = (be) nosey.
2. To ask about other people business or to try and find out about things that do not concern you. English = pry.
3. To be interested in things and eager to learn as much as possible about them. English = (be) curious.