Okay you can have 2 types of LiveUSB
1) A LiveUSB where everything is forgotten when you reboot .. think of it like an unwritable CDROM .. so if you create a text file on the desktop, or enter your wireless key, or browse the web, when you next reboot too the LiveUSB the text file will NOT be on the desktop, you will need to re-enter your wireless key, and the browser will have no memory of where you've been or any addons you installed.
This is great for security, and okay for a simple installation media, but pretty useless if you want to save files or install apps and not have to redo them next boot.
2) A LiveUSB "with persistence" .. this type of LiveUSB remembers your changes, so the file would still be on the desktop, your wireless key wouldn't need re-entering, the browser would remember your history/etc. and any installed apps will still be installed.
Now bear in mind that all these "changes" are saved to something called a "persistence file" that is layered on top of the normal (unwritable) Live image amd you get what a "persistence file" is.
Also bear in mind that the file system used for LiveUSB's is FAT32 so there's a limit to the size of a persistence file .. simply because FAT32 doesn't allow files larger than 4GB
So if you want your LiveUSB to remember changes, include a persistence file of "up to" 4GB.