A chef or cook (especially in high-end Japanese cuisine such as a ryōtei or sushi restaurant). Refers to a skilled Japanese-style cook.
あの旅館の板前は季節の魚を使った会席料理が評判だ。
The ryokan's chef is reputed for kaiseki dishes using seasonal fish.
板前として十年働いた経験がある。
I have ten years of experience working as a chef.
寿司屋の板前が目の前で握ってくれた。
The sushi chef made the sushi right in front of me.
The original meaning: the area of a kitchen containing the chopping board (the cutting/working area). Nowadays the occupational sense is more common.
寿司屋では板前の後ろに板場がある。
In a sushi restaurant, the cutting area (itaba) is behind the chef.
昔は小さな料理店でも板場が中心だった。
In the past, even small eateries had the cutting area as the center of the kitchen.