Question

Can i make a service which recognize voice even when phone is idle or screen off? I mean can phone listen to what the user will say even on idle state.

Answer 1

This is the entire program on how to make that happen.

http://developer.android.com/guide/topics/media/audio-capture.html

That shows how to record audio, the same implementation could be used to listen for audio.

Also, DEV GUIDE on what services are.

Right from developer.android.com

A service is a component that runs in the background to perform
long-running operations or to perform work for remote processes. A
service does not provide a user interface. For example, a service
might play music in the background while the user is in a different
application, or it might fetch data over the network without blocking
user interaction with an activity. Another component, such as an
activity, can start the service and let it run or bind to it in order
to interact with it. A service is implemented as a subclass of Service
and you can learn more about it in the Services developer guide.

This should give you all the information you need:
http://developer.android.com/guide/topics/fundamentals/services.html