I'm lost in the woods here. What's the definition of "we do not recommend running SMF 2.1 on a production site"? I currently have a forum. Is "production site" mean one being currently put together? Not familiar with that term.
dont use 2.1 in your currently running active forum. only use it as a test site to check out the new features.
"Production" is a term that, software-wise, refers to a stable and normally operating platform.
To make a comparison: imagine that you own a webserver, hosting several customer sites. You will want to run a final, non-beta version of whatever operating system supporting it. If you use an operating system in beta stage, your server might run into issues that would affect your customers.
Same as with your forum: it runs a stable version of SMF. Hardened, tested, stable. It's a live and working "production site".
You would not want to have your forum running a "in-development" beta version. Any bugs or security issues that might affect SMF will have a direct impact on your forum. As a result, it might crash or become unavailable.
I currently have 1.1.20. So it's not recommended to upgrade to 2.1?
It's not. 2.1 is the first beta release so it's prone to have bugs and incomplete features.
When 2.1 goes final, then you should consider the upgrade, especially because we will cease support for 1.1.x at that time ;)
or consider upgrading to 2.0 in the mean time. if your host upgrades to php 5.5 your forum will stop working. 2.0 will work with php 5.5.