Gordon Freeman is the silent protagonist from the Half-Life video game series, who Bernard is sent to capture during the second season of Catching the G-Man (renamed Catching the Freeman for that season).
The G-Man was Gordon's former employer. During the second season G-man sent his enemy Bernard and his friends to capture Freeman. Although Bernard believes he has captured Gordon Freeman in City 17, this turns out to be a double and he ends up being attacked by the real Gordon Freeman.
Freeman later made cameos in season 3 and 5.
Bernard is sent back in time to when the series started, therefore at that point Freeman hadn't yet arrived in City 17.