According to the spec:

These constants are defined mostly to make serialization of infinite/NaN values simpler and more obvious, but can be used to indicate a "largest possible value", since an infinite value gets clamped to the allowed range. It’s rare for this to be reasonable, but when it is, using infinity is clearer in its intent than just putting an enormous number in one’s stylesheet.

Final boss of z-index

We use it in Tailwind CSS v4 for pill-shaped borders:

  .rounded-full {
    border-radius: calc(1px * infinity);
  }

...as opposed to what everyone has done historically, which is pick some arbitrary huge value like:

  .rounded-full {
    border-radius: 9999px;
  }

No real practical benefit, just satisfyingly more "correct".

Selling pixels at a dollar each to make an Infinity Dollar Website™.