Alright. I'm going to be very blunt, and put it as simply as possible, in the hopes that you will somehow manage to put this together.
Black Mesa Source, is a modification to Source engine games. However, the changes are so vast, as it is an attempt at a remake of Half Life, it is more akin to being it's own game.
If you own ANY source engine game, such as Half Life 2, Team Fortress 2, Portal, Half Life 2 Episodes 1 & 2, and so on. You will be able to install and play Black Mesa Source.
If you do not own any source engine game, you can download and install the Source SDK, and play Black Mesa Source.
This means, that no matter what, if you have a computer that meets the minimum specifications to play Black Mesa Source, you can play.
If you cannot understand it at this point, then I cannot help you, and I advise you seek the nearest assisted living center.