Question: What is "script"?
This is a piece of code written in the Pascal-like language. FR can run such code - it gives you ability to change the report's behavior during the building process. See the documentation for details.
(does a band have a script?)
Yes, it does - select the band and select "OnBeforePrint" property in the FR Object Inspector (or press Ctrl+Enter).
(does a page have a script?)
Yes, it does. Click on empty space of the page and select "OnBeforePrint" (OnActivate if the page is the dialog form) property in the FR Object Inspector.
(can I access objects from the script?)
Yes, you can - use full name of the object:
(what properties can be accessed?)
Complete list of properties is in the documentation.
(I have two objects on a band, which script will run first?)
Object that you've created first will run first (that called Z-Order). Preferred way is to write a script in the band.