Offline map is available only in GPX Viewer PRO. So this how to won't work in free version of GPX Viewer.

GPX Viewer PRO currently supports only offline vector maps based on OpenStreetMap data which can be downloaded directly in GPX Viewer PRO. For adding custom 3rd party offline map data, please follow instructions in How to add custom offline map data

Below are step by step instructions how to use offline map.

1. First off you need to start GPX Viewer PRO.
2. In top toolbar tap on map button without globe. If you have hidden this button previously, tap on … button in top right corner on this top toolbar. In shown menu tap on Offline map. If you have also hidden this button, open left main menu, then tap on Settings button. In settings screen tap on Maps button. Then tap on Offline map data manager button, when you do this you can continue to step 4 of this how to.
3. In Offline map dialog click on Download button at bottom.
4. In Offline map data manager tap on + button in bottom right corner and tap on Worldwide low zooms map data. In shown dialog tap on OK button. This map data are only low zoom data for the whole world. You also need to download detailed map data for a country or a region. To do this, navigate to that country or region in shown directory structure and download it.
5. Then go back to map screen.
6. In top toolbar tap on map button without globe. If you have hidden this button previously, tap on … button in top right corner on this top toolbar. In shown menu tap on Offline map.
7. Tap on switch button in top right corner of Offline map dialog to enable offline map mode. In shown list you can also select different offline map style. Then tap on OK button.
8. GPX Viewer PRO will switch to offline map and show it on the screen. If no map is shown, try zoom out to world level zoom and then try to zoom in.

Below is video showing following instructions above: