An island anim cutscene is the cinematic cutscene you see playing in the OFP main menu's background after you've played a mission and have returned to the OFP main menu. While not required, the vast majority of island addons come with one or more such cutscenes.
Without AMORE, island addon makers who produced island anim cutscenes could only use OFP's internally defined music and sound files within those cutscenes. This is because OFP does not process file DESCRIPTION.EXT in an island anim's mission folder. Without AMORE, there is no other file, other than DESCRIPTION.EXT, where custom audio files can be defined.
However, with AMORE, since custom audio files are no longer defined in file DESCRIPTION.EXT, island addon cutscenes can now include customized music and sounds.