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 a slow internet connection, you can download maps directly via PC and then transfer them to the MAPS.ME folder on your device. On Android maps (.mwm files) are stored at MapsWithMe folder. On iOS, you need to connect your device to a computer and copy maps via iTunes (select your device, then Apps – scroll down the page, select MAPS.ME and copy maps to Documents section). Don’t forget to restart your device. Please note, that even the latest maps will be marked as outdated if you download them via PC.