My Maps is one of Google's applications and whilst it is based on Google Maps, it also has a stand alone app. You can create your own maps and share them with other people. This blog outlines some of the features of My Maps.
The Google My Maps Help page is a useful place to start creating. The tutorial below has no voice over but goes through all the main functions of creating a map.
To create a map you need a computer and you can add others as collaborators. Once made you can share with others and they can access the maps on any mobile device.