clsx is generally used to conditionally apply a given className

This syntax means that some class will only be applied if a given condition evaluates to true

const menuStyle = clsx({
    [classes.root] : true, //always applies
    [classes.menuOpen] : open //only when open === true
})

In this example [classes.menuOpen] (which will evaluate to something like randomclassName123) will only be applied if open === true

clsx basically outputs a string interpolation. So you don't have to necessarily use it, although is a common practice.

There are many supported syntax that you can check in the official docs

Instead of

<div className={`${classes.foo} ${classes.bar} ${classes.baz}`} />

You can use it like this

const { foo, bar, baz } = classes
const style = clsx(foo, bar, baz)

return <div className={style} />

Many people already explained it pretty well. I still wanted to add an example containing className. In the example you can see different classes, applied if a given condition evaluates to true. In the example you can apply a class with a boolean value, a boolean variable or a compared string (If match, return true). The class classes.drawer is always applied and does not depend on a condition.

className={clsx(classes.drawer, {                  // classes.drawer is applied always
          [classes.drawerOpen]: true,              // classes.drawerOpen is applied always, bool = true
          [classes.drawerClose]: !open,            // you can also use boolean variable
          [classes.drawerRed]: colorVar === 'red', // you can also use string variable
        })}

classes.appBarShift will be applied only if open evaluates to true. If the array has more classes all of them will be applied if open evaluates to true