To export the HEAD of your current branch (the one with an asterisk before it, on ‘git branch’ command’s output) in your git repository, do the following:
git archive HEAD | (cd ~/somedir_where_to_put_it/ && tar -xvf -)
Provided that ~/somedir_where_to_put_it already exists, otherwise, mkdir it.
Instead of HEAD you could use any revision’s hash number and then the codebase as it was in that commit would then be exported. To obtain such hash number read git log’s output.
Note: tar -xvf - is the command that consumes the subshell’s (delimited by the parenthesis after the pipe) input. It extracts a tar content from stdin (represented by the minus symbol at the end of the command, before closing the parenthesis) which was provided by git archive, thus, it is possible to conclude that git archive provides in its stdout a.k.a. standard output stream, the contents of the codebase at the given revision, in tar archive format.