It's a computer analysing the images apparently. Another option was putting little chips in the shirts, but the downside was that the position of the shirt would determine wether it was offside or not and not the player. They countered this by still having linesmen, who would hear a click if the system said it was offside, but could overrule it if they were very sure. This leaves room for error though, so in these cases a video ref would be used too.
Anyways, everything is better than watching millions of replays and seeing that it was or wasn't offside.