A random binary tree is like a real tree. It has branches coming out of a single main trunk that branches off into two more branches. But the difference is, instead of having branches that always grow in the same way, like a real tree, the branches of a random binary tree go different directions at random. It's kind of like if you were blindfolded and playing connect-the-dots, you wouldn't know which line was going straight, which was going left, and which was going right. That's how a random binary tree works... it's just connecting branches going different directions in a random way.