Your download can fail due to a temporary network error or specific network provider/router settings. Please try again later or use a different Wi-Fi access point. In addition, make sure, that you have enough free space to download maps.
If you have Android 6 or higher, please make sure that you have granted storage permission for MAPS.ME (usually, it enabled by default) in your device settings → Apps → MAPS.ME → Permissions → Storage.
If you have a slow internet connection, you can download maps directly via the direct link and then transfer them to the MAPS.ME folder on your device.
On Android maps (.mwm files) are stored in MapsWithMe folder.
On iOS, you need to connect your device to a computer and copy maps via iTunes (open iTunes → select your device → File Sharing → select maps.me and copy files to maps.me Documents section). Don’t forget to restart your device.
Note: even the latest maps may be marked as outdated in the app if you download them via direct links.