The parentheses enclose expressions, and the hierarchy of expressions builds a tree. This tree, in effect, is your program's AST.

"Add x y z" is exactly what it sounds like, if I said those words to you. The add function is usually +, so (+ x y z) is an expression that adds x, y and z, and the whole expression evaluates to the result. You can nest expressions however you like, so, for example, (+ x (* a b)) adds x to the result of the expression (* a b), which evaluates to the result of multiplying a by b.

You can put arbitrarily powerful code inside an expression, and you can use an expression absolutely everywhere you can use a value. Any one of +, x, or y, could be replaced by an arbitrarily complex expression (yes, the function too - you could replace it with a call to a higher order function, which would return a function that is then called over x and y).

The neat thing is, that's basically[0] all the syntax Lisp has. There are no reserved keywords. There's no magic to math or control flow, they all work as per above, and can all be redefined at will. You can make + subtract. You can change the language's if and else to work any way you want. You can redefine Lisp's reader to change the syntax of the language to absolutely anything you like. And you can do all of this in a running REPL without even needing to restart it. That's the power of a Lisp.

If you're interested, read Common Lisp: A Gentle Introduction to Symbolic Computation by David S. Touretzky.

[0] Macros are the other piece of the puzzle, but to understand them you would need to read up on Lisp more.