Verizon added the Glympse feature to their messaging app last year as part of a series of significant upgrades and enhancements to the app. The G icon you see next to a "where are you?" message is a feature they included to highlight the easier way to coordinate location with someone with whom you are texting with.
It's important to note that even though the Glympse feature is a part of the Verizon Messages app, the feature is inactive unless you explicitly choose to use it. A core tenant of Glympse is that users are always in control of when their location is being shared with anyone. This means that unless you specifically choose to share a Glympse with someone, the feature is essentially disabled meaning that your location is not collected nor is it shared with anyone. Also, a Glympse has an auto-destruct feature so that when the timer on the Glympse expires, your location is no longer visible to anyone.
More info on the feature is available at the links below.
How to use Verizon Messenger: http://www.verizonwireless.com/support/how-to-use-verizon-messages/#glympseoff
Article on new Verizon Messages enhancements: http://gigaom.com/2013/10/25/thanks-to-glympse-verizon-customers-can-coordinate-their-location-via-sms/
Video walk through of Glympse feature in Verizon Messages: https://youtu.be/LQVZGOLWZ78