Any grayed out track with a cloud symbol to the left of it in Media Library means that the file is not actually stored on your device, and only iCloud has a copy which only happens with tracks purchased from the iTunes Store or if you have iTunes Match or Apple Music turned on in the Settings of your iPhone, iPad or iPod Touch. To find out if you have either music cloud service enabled, you can tap Settings > Music and look there. With iTunes Match and Apple Music, it doesn’t download the file until you actually try to play it, so please check on your device to see if that’s the case. They should all have cloud icons next to them in the Music app, and iExplorer can only transfer a song if the audio file for it is physically stored on your device. The same goes for Purchased tracks. By default, iOS doesn't download the media file until you decide to play it.
If that's the case, and they are Purchased tracks or you do have either of those cloud services turned on, you'll either need to download the songs to your device by tapping the cloud icons with the down arrow which you can do for entire albums and the try using iExplorer again (after closing and reopening it or disconnecting and reconnecting your device), or you could just open iTunes and sign in via the Account menu with your iTunes/Apple ID and if they are just purchased tracks, they be added as cloud tracks (not downloaded to iTunes yet) or if you have either of Apple's subscription services, turn on Match or Apple Music using the Account menu.