Play Music is the music app linked to your Google account. It streams things from their cloud servers. You can upload up to 20,000 of your own songs for free onto it, which is nice. However this requires you to be connected to the internet.
If you want to just put music on it locally (on the storage), just plug it into your computer with the USB cable, open up 'Computer' and it should show your Nexus 7 as a media storage device. Then you can put your music wherever (I recommend the Music folder
), and then open up a media player. I think Play Music can play local content as well - otherwise, there's tons of apps you can search for that will play music in the Play Store.