The Wolfram Language handles many different kinds of things: mathematical formulas, lists, and graphics, to name a few. Although they often look very different, the Wolfram Language represents all of these things in one uniform way. They are all expressions.
You do not always have to write expressions in the form f[x,y,…]. For example, x+y is also an expression. When you type in x+y, the Wolfram Language converts it to the standard form Plus[x,y]. Then, when it prints it out again, it gives it as x+y.
You can see the full form of any expression by using FullForm[expr].
The object f in an expression f[x,y,…] is known as the head of the expression. You can extract it using Head[expr]. Particularly when you write programs in the Wolfram Language, you will often want to test the head of an expression to find out what kind of thing the expression is.
|Head[expr]||give the head of an expression: the f in f[x,y]|
|FullForm[expr]||display an expression in the full form used by the Wolfram Language|