A fencer is a person who does fencing: the sport where two people “fight” with long, thin swords. They are not trying to hurt each other for real. They wear a mask and a thick jacket, and they score points by touching the other person with the sword. It is a school sport and an Olympic sport. The swords have special names (foil, épée, sabre), but the person is still a fencer in all of them. The word is everyday sports English, not slang and not especially formal. Though actually, the first picture many learners get is wrong: this is not a person who builds a garden fence. That is a different “fence”. A fencer is the athlete.