To make it simple:
In OS 9, Applications had most of their needed libraries either bound into their code or they got them from system extensions.
"Libraries" might not be the correct term under OS 9, but I'll use it to make things easier. I don't know if you are a programmer, so I will try to explain it. I do this because I want to help you, not because I think you are an idiot.
When you code something, you use libraries. It's like a real library. You use the knowledge of others. Easy example: you are writing an app which can open files. Normally, you would have to write your own methods/functions to make the graphic card draw a window, you handle any mouse/keyboard events in the "open file" window, to analyze the file system etc. etc. This takes time. So, what else can you do? You pull a book out of your library (in this case the book would be a function) and you use it's knowledge (the "actions" the function executes) to do this file opening. Result? You are saving time, you are securing that it works (since in this case the functions have been already written by Apple) and all applications share the same "open file" functionality, so debugging is easier, the final user finds it easier (since each app more or less has the same "open file" dialog) etc.
Now, there are two possibilities when you code: either include these libraries static. This means they are "hardcoded" into your application, making it big. The other approach is that you dynamically load these functions from system libraries. You might know that Windows uses files with the ending .dll, which is exactly this, it's a dynamic link library. So any app which uses our "open file" dialog executes a function withing this library to display the window and make it work with the app.
It saves space since all apps are smaller, they share the same functionality over one file, a system library. These libraries have to be present in the RAM when the application runs, everything else would be slow. So once the application starts, it searches all libraries it needs, loads them into the RAM, and the starts running. What the prebinding does is making some kind of list where the needed libraries for each app are, making app launch times faster. If the prebindings are out of date, the application would start to search the library all over you harddrive before it is able to start running.
This is a VERY basic explaination, and I know that there are "errors" in it, I just wanted to explain what this prebinding stuff is and how important it is.