How do I pass data between Activities in Android application?

The easiest way to do this would be to pass the session id to the signout activity in the Intent you’re using to start the activity:

Intent intent = new Intent(getBaseContext(), SignoutActivity.class);
intent.putExtra("EXTRA_SESSION_ID", sessionId);
startActivity(intent);

Access that intent on next activity:

String sessionId = getIntent().getStringExtra("EXTRA_SESSION_ID");

The docs for Intents has more information (look at the section titled “Extras”).