It specifies whether or not apache should follow a simbolic link while looking for a file. For example, if you have a file /home/mydomain/www/myfile.html which is a link to /home/mydomain/somedir/therealfile.html
Then apache will only retrieve the realfile.html if you have that option enabled.
In some (or all?) server configurations, mod_rewrite requires FollowSymLinks to be enabled, or it will crater with a 500-Server Error.
If your mod_rewrite code works without the Options +FollowSymLinks directive, that means that your server configuration file has enabled them already, and you won't need that directive in your .htaccess files.
I try to remember to include it in posts here anyway, just so someone asking mod_rewrite questions won't have a problem, and either give up, or have to post again.
I believe you would call it a "Shortcut" in Windoze-based environment.
The requirement for enabling FollowSymLinks is not well-defined. The only way I learned about it was because I got a 500-Server Error the first time I ever enabled mod_rewrite, and the error log entry said something to the effect of, "You must enable SymLinks for this to work."
I include it in posts mostly so I don't forget to warn that it may be required...