I did a lot of features as a reporter, and music was often a big part of my stories. There always seemed to be some lyric, or some instrumental, that fit. "Wipeout" was perfect for a piece on a surfing dog, "At the Hop" took a story about hula hoops to the next level. I realize those are old tunes and I'm dating myself. The point is, music can put you in a time and place that fits the story.
It can also act as a bridge, like a nat sound break. A long package that changes course moves faster with some quick cuts in the middle. A fast instrumental can add energy when edited under the quick cuts, making them seem even faster.
Before you start searching your record collection for appropriate music (note: rap isn't music and will turn off any viewer over 40), you need to check with your News Director to find out if you have the rights to use music at all. Some stations pay a flat fee to ASCAP for the right to use any music. Others use a pay as you go system called a "needle drop" method of accounting. Every time the needle hits the record (again, a dated term, but you get the idea) the station would pay for the rights to the music. And there are some stations that do not pay for music at all. If you're working at the latter, you're out of luck.
Photogs are great at picking music, as they seem to have a sixth sense for knowing what tune fits their video. If you're working with one, ask if a bit of music would make the package better.
Obviously, music is inappropriate for many stories. You don't use it to cover murders, fires or wrecks. But a soft piano instrumental can add emotion to a touching story, a quick one can bring energy to a package.
The best illustration of the latter is on CSI. Each week there's a point in the show when all the lab techs go through the paces to analyze evidence. It would be deadly slow without music, but they always add something fast paced to move things along,
You can do that in the middle of a package with your b-roll.
A music bed is also useful to add a mood or energy. You can use it as an extra track, blend it with your nat sound.
Too many packages these days are simply sound bites and voice track. Natural sound adds a ton to any story, and music is yet another element that can take your stories to the next level.
If there's a song stuck in your head while you're doing a story, maybe it belongs in the story.