When you speak of someone having clout, it usually means that they communicate a sense of power or influence, particularly in the political sense. "You’ll wanna talk to that big guy over there if you want me to let you in. He’s got clout."
Clout can also mean to hit someone really hard — either the hit you give (“that’s a big clout he just landed”) or the act of hitting (“she clouted him with a baseball bat”). Of course, the sense of having power and the actual hitting are related, since clout is something to be wielded — either physically or figuratively. Note: it's not just tough guys who have clout. China is said to have "growing economic clout," and Oprah is known to have significant clout in the media industry.