I have frequently heard in pop music to use the technique described above: to start a song with a melody in a certain key and, after a while, to play again that melody raising the key one semitone.
For example, this is done in the next song (I can not remember right now a better example), where melody starts in the initial key at 0:38 and thereafter starts in a semitone upper one in 1:17:
Has this technique a particular name? Are there any specific rules to use it?