By default, the app will attempt to load the online EOTopo map when you first launch it. You can change maps by pressing the icon in the top right of the map window - the map layer button. You can select from any of the 3 available online maps or select the offline map labelled EOTopo.
If you get a blank map when you select offline - then check that you have downloaded the base map - check this by going to the Data Manager. You must download the base map and if you have bought Premium Maps then you also need to download them for the extra zoom levels to appear.
Note - each time you open a map window it will remember the last map-type selection and load that so always check the map layer is correctly selected.
Look for the red line at the bottom of the map alerting you to "More Detailed Offline Maps Available". If you see this, then you have not yet downloaded the most detailed map available in the Premium pack for the area you are currently viewing. Go into the Data Manager and see what files have not been downloaded and you can add them at any time.
Another offline map use tip: turn off your phone's mobile data - rather than using flight mode. Flight mode turns off many things including the GPS! You must have GPS enabled to use the app.