Basically, you create a Glympse and send it to someone or a group of people, and they can observe your progress as you travel. You can set a time limit for the Glympse and/or you can set a destination and end the Glympse when you get there.
The uses crop up the more you use it. My friend D, who introduced me to the app, uses it because she's always late and sends a Glympse rather than text in the car while driving ("I'm 10 minutes away!"). My family and I use it when we're traveling back and forth. My dad knows where I am en route and then knows I've arrived home (I forget to call and say I got there safely; I'm a bad kid). My SO and I use it when we leave work at night, because sometimes we have plans afterward and both have commutes.
And no, none of this is really necessary. Texting or calling would really do the same thing. It's just handy to send a Glympse and be done with it, and if you're driving, it's a lot safer.
Here is a quick tutorial on how to make a shortcut to frequent Glympses so you can tap directly on an iOS icon and send a Glympse instead of starting the app and making one each time. I don't know how this works on other platforms.
Create a Glympse shortcut in iOS
Fire it up, tap the big blue "G," and swipe to the far left icon
Fill stuff in
Enter the person's name (or group name or whatever) at the top, set the slider to the amount of time you want, and set the optional stuff at the bottom if you want (I leave those blank because I want a general use shortcut)
Tap the star at the very bottom
Type in your shortcut name (important if you're making a few, like "Leaving work" and "Leaving house") and then tap "add to home screen." Otherwise "done" favorites the Glympse within the app
Follow the breadcrumbs
Glympse will shuttle you over to Safari for some behind-the-scenes magic; just follow the prompts
Wrap it up
Tap "Add." You can change the shortcut name if you want here. An icon will appear on your home screen. Tap to easily send a Glympse!