Flight Following allows ATC to track you during your flight and will advise you on things like air traffic, barometric pressure, ect.

Like IFR flying with more flexability.

As always, thank you kindly.

So as long as we're on the subject, I was about 25 miles southeast of Des Moines last night, and they handed me off to Minneapolis Control.  Was that a glitch or is there something I'm missing?

Dread.
I think Minneapolis Center actually does cover Des Moines airspace. And Andrew is right. They don't care what your destination is, they're just tracking you while in they're space.

You might also notice that ATC will have you contact the same Center, several times on different frequencies while you're in their airspace.
Some times only a couple of minutes apart.

I don't see the sense in that, myself. 

You know us newbies just need someone to hold our hand crossing the streets in the sky.

Phil

No need to re-hash what has been said, but just to add a point about why they keep handing you off to the same Center:  Center (and Approach too) often distibute the work load by dividing different segments of the airspace into smaller areas internally, so a given controller has fewer planes to watch.  These are often based on geography (so one controller freq. covers North of the area south, for example).  Thus if you are just crossing over the airport you might go from one controllers to the other.  And if there is an airport in the area, you might go from the center to approach (as you pass over the TCA for the area) and then back to center (as you leave the TCA once again).