I am completely new to bluetooth app development. what exactly is a bluetooth profile? is it a hardware specification for the device? can an android mobile phone with bluetooth act as sender and receiver in A2DP profile?
A bluetooth profile is a specification on the protocol and functionality of a bluetooth device. It is not just a hardware specification, because implementing a profile will often depend on both the software stack and the hardware chip. You can find more information from the wikipedia page.
And in the case of A2DP, it is specifically designed for music streaming. It cannot be used for arbitrary data communication (if that's what you mean by "sender and receiver"). If you are looking for a generic data communication mechanism over bluetooth transport, the Serial Port Profile (SPP) is what you need (some people also call it RFCOMM). Android SDK user guide has quite detailed information on how to use RFCOMM API: http://developer.android.com/guide/topics/wireless/bluetooth.html