"Sy" is a special form of "Bod". I can't fully explain it but it sort of means "who is".
Have I got this? The normal, unemphatic form of the sentence would be: Mae Dewi Lingo'n pysgota heddiw. By fronting Dewi Lingo, we emphasize that it is he who is fishing and it becomes Dewi Lingo sy'n pysgota heddiw.