Studying some classes of Android, I realized that most of the variables of methods
are declared as final.

Example code taken from the class android.widget.ListView:

/**
* @return Whether the list needs to show the top fading edge
*/
private boolean showingTopFadingEdge() {
    final int listTop = mScrollY + mListPadding.top;
    return (mFirstPosition > 0) || (getChildAt(0).getTop() > listTop);
}

/**
 * @return Whether the list needs to show the bottom fading edge
 */
private boolean showingBottomFadingEdge() {
    final int childCount = getChildCount();
    final int bottomOfBottomChild = getChildAt(childCount - 1).getBottom();
    final int lastVisiblePosition = mFirstPosition + childCount - 1;
    final int listBottom = mScrollY + getHeight() - mListPadding.bottom;
    return (lastVisiblePosition < mItemCount - 1)
                     || (bottomOfBottomChild < listBottom);
}


What is the intention of using the final keyword in these cases?

I would say that this is due to force of habit. The programmer that wrote this code knew as he was writing it that the values for the final variables should never be changed after assignment, and so made them final. Any attempt to assign a new value to a final variable after assignment will result in a compiler error. 

As habits go, it's not a bad one to develop. At the least, making a variable final specifies the intent of the programmer at the time of writing. This is important as it might give subsequent programmers who edit the code pause for thought before they start changing how that variable is used. 
