A private LUN is one that is used by the system and is not available directly to any host (you can't put it in a storage group). Some examples of private LUNs would be the LUN on a Global Hot Spare and an element of a MetaLUN.

So, that leads to the question of what exactly a MetaLUN is. In the simplest terms, a MetaLUN is a LUN that is made up of multiple "elements" (LUNs). The easiest example would be to think about a host that wants a single 200GB LUN allocated to it. You only have 100GB available on a single RAID group, so you look further and find a second RAID group with another 100GB free. Since you just want to allocate a single LUN to the host you build a MetaLUN by extending the first LUN with the second one. You end up with something that can be allocated as a single LUN but it looks like a single 200GB LUN to the host.

There are two kinds of MetaLUNs, and they are ideal for different applications.

Concatenated MetaLUNs are good for building a larger LUN from multiple smaller LUNs when you aren't so concerned about performance characteristics. It is just like a spanned volume on a Windows host... you just "tack" the new chunk of storage on the end of the existing LUN.

Striped MetaLUNs can allow you to build more performance potential into a LUN. Let's say you need a 200GB file system for a database. You know you are going to be driving very high IO through this file system... more than you can get out of your standard RAID5(4+1) RAID group. Instead of building a single LUN on a single RAID group you would build 4 x 50GB LUNs on four separate (but preferably identical) RAID groups. You then build a Striped MetaLUN with the four separate LUNs and end up with something that can potentially support 4 times the IO throughput.

This is a simplification, and there are lots of variables and best practices to consider... but this should get you started.