These are leitmotifs. Wagner made them famous. Give a single person, place, or even feeling it's own theme or in some cases just a chord (the "Tristan" chord from Tristan und Isolde). You should pay attention good soundtracks to anything and you'll be able to catch very, very subtle use of this through abstracting the original tone set or rhythm in an almost unrecognizable way and laying it over something else.

In a Wagner opera you might have something like a theme of one person, and another person, and a love them, and a strife theme and they would all be layered differently throughout the orchestra to signify the people's attraction and the turmoil it causes. It can be used to say without words that one person is thinking of another person.

Nobuo Uematsu uses it frequently, but usually not in such complex ways. Mostly he just gives a person or place (or thing or feeling) a very obvious theme and then makes a sad version or a more upbeat version. Less subtle hints and more blatant stuff.

But leitmotifs are everywhere and if you're listening for them in movies and even in some TV shows you may get a hint of extra depth about the plot that's not spelled out in the actions or scripting.