If we are speaking of striking strength, it is primarily a result of proper end point timing. The more efficient and completely the body mass/weight is used, the more power/strength in the strike.
Partially, but strength always matters. There is a reason you see more KO's in heavier weight classes, even though you often see better technique in lighter ones.
This is all true, but strength CAN get in the way.
As Dave says, the ability to efficiently bring the body mass into the deliverance of the strike will result in a much stronger strike without the need to have tremendous strength, and without needing to apply a huge muscular effort.
Someone with tremendous strength, who relies on it alone without efficient use of the full body (I am simply illustrating an extreme example, not saying that I believe people actually do this), can hit as strongly, but to do so he needs to be that much stronger, and he needs to put in the muscular effort. The thing is, most people just aren't that strong, so the strongmen are the exception who can get away with relying on strength.
But if you use proper techinque in bringing your body mass into play in the strike, it often works better if you are relaxed and make minimal muscular effort. In this case, if you try to "muscle" the punch thru at the same time, it can actually work against the technique. In effect, the act of making the tremendous muscular effort can sort of "separate" the arm and shoulder from the power potential of the full body torque. When that happens, you are back to simply relying on the muscular strength of the arm and shoulder, and you deprive yourself of the greater power of the full body.
This is not to imply that by being relaxed you need to turn into Gumby or something. Obviously you need to engage enough physical strength that the body and striking platform are stable. I'm just saying that if you get the technique right, it actually works better if you don't try to muscle thru at the same time, and you don't tire yourself out nearly so quickly.