If statements, boolean algebra,AND NOT OR

Reading the tutorial on if statements, lesson two on cprogramming.com has made my face melt.
I am horrifically thrown off, and no matter how much I reread, or try to understand, my brain is mushed, and I can't process it.
I even tried reading aloud.
Can some one break these topics down Barney style for me?
If you can, that would be most appreciated.

 

The simple is thinking logically

Code:

if(some condition is true)
{
  The following lines will be executed
}
else
{
  The following lines will be executed
}