It looks like you're on Airplane mode. I believe Free users can only stream music. Songs being grayed out, could be because the song might not be available in your country. If you have friends using Spotify, you might want to ask them if they could see and play these songs that are greyed out.
If a song is greyed out, it means that song is currently unavailable and this maybe due to a lot of reasons ranging from licensing issues to region restrictions. Spotify would love to have all the world’s music available to everyone. However, some artists and tracks aren't currently available but keep checking because Spotify works everyday to add new music!