In the context you have shown, it @is at the beginning of the argument to the --datecommand date:
date -u --date @$((`date +%s` - $date1)) +%H:%M:%S
In this case, this means that the argument should be considered as the number of seconds since the era, see the example in man date:
(1970-01-01 UTC)
$ date --date='@2147483647'
$ date -u -d @0
Thu Jan 1 00:00:00 UTC 1970
@ date, bash.