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.
Also, if you have very outdated maps and the app can't update them, it may help to delete outdated maps and re-download them.