A file with .hqx at the end is encoded by a somewhat obsolete method called "binhexing". The reason this is done is that when Mac files are uploaded and downloaded from the internet, they can lose important info, such as resource forks. By binhexing, the file is converted into a format that will remain intact.
The problem with binhex is that it substantially increases the file size-- about 20%. As a result, encoding with MacBinary has become much more popular. These files have .bin at the end.
Either way, to decode the file, use StuffIt Expander.