What exactly does "system managed size" mean for a Windows pagefile?

It does exactly what it says on the tin: the OS manages the size of the pagefile, which can shrink or grow dynamically. The lower and upper bounds are 1x your RAM size and 3x your RAM size or 4 GB (whichever is larger) as explained more elaborately here. The pro is that you don't have to worry about sizing your pagefile, the con is that your pagefile can become fragmented.

Where it is useful is in exactly the situation it's designed to avoid: sizing your pagefile. You can set it to System Managed and check in every several minutes (via a script), recording the smallest and largest sizes it uses over a typical usage period of a month or so. You should then have a very good idea how large to manually set your pagefile to be.

Near the end of this article, Mark Russinovich briefly discusses system-managed pagefile sizes:

You’ll notice that the default configuration is for Windows to automatically manage the page file size. When that option is set on Windows XP and Server 2003, Windows creates a single paging file that’s minimum size is 1.5 times RAM if RAM is less than 1GB, and RAM if it's greater than 1GB, and that has a maximum size that's three times RAM. On Windows Vista and Server 2008, the minimum is intended to be large enough to hold a kernel-memory crash dump and is RAM plus 300MB or 1GB, whichever is larger.

The rest of the article is well worth reading, and does talk a bit more about what happens when Windows grows the pagefile.

In my own experience, system-managed pagefile is the best option to take in the vast majority of cases.

The general rule for system managed pagefile is: the operating system will create a page file that is one and a half times the amount of RAM that is installed in your computer.

However you rarely need the size of the pagefile be determined by system because nowadays computers RAM is more than adequate. A system managed page file with its shrinking and growing is subject to heavy fragmentation.

This KB article addresses the issue and explains how to calculate the page file size: How to determine the appropriate page file size for 64-bit versions of Windows Server 2003 or Windows XP.

Setting to a fixed size pagefile is worth considering. Additionally, it prevents this problem: The page file size may become alternately too small or too large when you start Windows Server 2008 or Windows Vista if there is no available free disk space, and the page file size is managed by the system

It handles sorting out the size of the pagefile. In the past I've set that when the available drive space is substantial. If you have the room why not let the system have as much as it needs?

I ussually set the size of the pagefile manually at about twice the size of the RAM Memory so the system won't take too much I/O time with excessive growing and shrinking of this file.