What language are apache .htaccess files written in?

There is no specific name for the syntax as a whole, but they are called Directives.

According to Wikipedia's page about .htaccess, the name of the language is a combination of the previous answers/comments to this question.

Format and language

.htaccess files are written in the Apache Directives variant of the Perl Compatible Regular Expressions (PCRE) language. Learning basic PCRE itself can help in mastering work with these files.

For historical reasons, the format of .htaccess files is a limited subset of the Apache HTTP server's global configuration file (httpd.conf) even when used with web servers such as Oracle iPlanet Web Server and Zeus Web Server which have very different native global configuration files.

Incidentally, "htaccess" is short for "hypertext access", and the . dot makes it a hidden file in Unix enviroments.