In basic, a script a web site written in php. You need linux web hosting to run them and there are plenty out there.
Correction: a script is a set of instructions Scripts can be used for almost anything and even specific to computers saying "a script" is far too generic. PHP is used for scripting - allowing the user to interact with a web server. True, PHP does require a Linux server. As for getting one in your website and activating it, it all depends on what you want it to do. You can have scripts to run a guestbook, count visitors, manipulate a database (generally MySQL) and so much more.
No.. you can write scripts with PHP but scripts do not consist solely of PHP. Scripts can be written in PHP, ASP, JS, etc. It's basically just, as was said, a set of instructions for a server to execute.
http://en.wikipedia.org/wiki/Scripting_language#Web_browsers ECMAscript is a script! Javascript is a script! scripts can be written in any language the browser or the server will understand: PHP, ColdFusion, Python, Ruby, PERL, ASP, and plenty more depending on how exotic your server setup is.
As I stated "a script is a set of instructions" and doesn't have to be a server. You can get scripts in almost anything. DOS and many applications have their own scripts even video conversion. Scripts can be absolutely anywhere.
scripts are basically small programs written in any scripting languages, like Perl, Python, java for generating a graphical user interface, validation on web forms and to get better results in the most readable form (e.g graphs, animations, web pages, video etc.)