Swipe down the notification shade and tap on the USB connection. Make sure MTP is selected. If there's a selection for "Mass Storage" or "USB Disk Drive," that's even better, but I'm not sure if that's available on the Nexus.
If you're on MTP, you still can't see every single folder--certain system folders will remain hidden. You could use a wireless solution like AirDroid or Wifi File Explorer to get a better look.