I'll try to clear some tings up for you. But first what iOS are you on? (I'm assuming iOS 4).
What Semi-Tether means: First let me tell you what a tethered jailbreak is: A tethered jailbreak means that when you need to reboot your device, you have to plug it in to your computer Open redsn0w, Shut off device, enter DFU mode, click "Extras" then click the "Just boot" button.
A semi-Tethered jailbreak is when you do not redsn0w to reboot your device. You can reboot your device, but after it reboots, it will be in a none-jailbroken state, where Cydia and nothing from Cydia will work. And Safari will not work either. However you can use another web browser, and calling and txting will work as normal too. You have to boot tethered in redsn0w to boot back up to your normal working jailbroken state.
As for the semi-tethered 5.1 jailbreak..Well you do not need the Semi-tether package to have a semi-tethered jailbreak. Mobile Substrate does that. Mobile Substrate is what allows things to be modified in iOS. It is installed automatically when you install literally any tweak.
The Semi-Tether package is suppose to do 2 things. It is suppose to protect your notification center widgets, and patch Safari so you can use when you reboot into a none jailbroken state. I have not tried it in 5.1, and I don't know if it has been updated lately but I found it was 100% pointless to install. Unless you cared about patching Safari, But you can use any other web browser from the app store.
So you do not even need the Semi-Tether package to have a Semi-Tethered jailbreak.
But as far as the semi-tethered jailbreak for 5.1 .......................Well it seems pretty stable to me from what i noticed on the one day I was on a 5.1 jailbreak.
On a side not, if you do jailbreak, you cannot install "anything" in Cydia. Not everything is made for iOS 5 or even an iPhone. Please make sure to check compatibility. And if a package does not say it is iOS 5 compatible somewhere in the info page, then do not install it. You can also check for this in the "Recent Changes" tab under most tweak's info pages.
Pretty much every newer tweak that has been released in the past few months were made for iOS 5 any way. But always do a search if you cannot find out on a tweak's info page.
Basically, as long as you follow directions exactly, check compatibility, you should have no problems.
and one tip I can share with you, is if you happen to install anything from Cydia that requires a reboot (like WinterBoard for example), then do not bother pressing the "Reboot Device" button. Just plug in your iPhone, open redsn0w, Shut off device, enter DFU mode, then click "Extras"> "Just boot" and you device will boot back up to your normal jailbroken state.
Good luck..........And I hope this cleared up a few things for you
