There’s a literal physical meaning which is to bring someone down to the floor. It’s used in wrestling or MMA/UFC for example. If you’re trying to capture King Kong you can yell out “Take him down!” to your men.
Then there is a figurative meaning which is to ruin, beat or destroy someone in the context of the completion you’re talking about. Examples:
You have a business competitor and you want to take him down. This means ruin him by trying to put him out of business.
You’re in a chess tournament and you can say you’re gonna take your opponent down. This means beat him.
You’re a cop and you can say you’re taking the criminal down. This means to destroy him by arresting him and putting him in jail.
You can also say « you’re going down » to an opponent, adveersary or competitor.