Samsung Galaxy Nexus has a 16GB internal memory and no external sdcard. I'm wondering if that means I have 16GB (or at least the free space left of that memory) to install applications?
Yes you have full 16GB for apps+data together in a single file system. You won't have to do any moving to SD card any more.
Google merged both partitions. It's just one big file system now with sections for the former parts. It's completely transparent, so no worries for you.
- Formerly: /data and /sdcard were separate partitions
- Galaxy Nexus / Nexus 7 and others running Jelly Bean: One single partition for both, i.e. no need to decide how to divide the space for both any more.
To make it more generic:
The partition layout will however not change for former phones (most probably), so devices which got upgraded to 4.x+ will still have separate file systems for both /data and /sdcard. If your device has an additional micro SD card this will also be separate still.
By the way: This is the reason why there's no USB-thumbdrive functionality any more for the Galaxy Nexus (because /sdcard is not a single partition any more and also there's no FAT32 formatted partition internally (except for SD cards if existent))