In my .htaccess file, this works

RewriteEngine On
RedirectMatch 301 .* http://www.newdomain.com/

But this does not

Options +FollowSymLinks
RewriteEngine On
RedirectMatch 301 .* http://www.newdomain.com/

What is the purpose of

Options +FollowSymLinks

and is it really necessary?

Incidentally is there anything wrong with using this command
to redirect everything from an old domain to the home page of a new domain?

RewriteEngine On
 RedirectMatch 301 .* http://www.newdomain.com/

Incidentally is there anything wrong with using this command
to redirect everything from an old domain to the home page of a new domain?

How does the server "know" which or what hostname to redirect??

Symlinks is Unix shorthand for Symbolic Links which are sort of equivalent to Windows "shortcuts" though decidely more useful. A FollowSymLinks option tells Apache to serve the content from the drive or folder that the SymLink references.
If all your documents are in the DocumentRoot of the virtual host Symlinks are not actually required.

the Options+ directive means you are adding the following option(s) to the ones specified in httpd.conf. Options- means you want to remove option(s) for the current directory and sub directories