What is the significance of keys in React?

Keys help React identify which items have changed, are added, or are removed. Example:

const numbers = [1, 2, 3, 4, 5];
const listItems = numbers.map((number) =>
  <li key={number.toString()}>
    {number}
  </li>
);

One of the tricky aspects I've found during the few weeks I've been using React.js is to understand the key property you're expected to pass to a component when it's part of an array of children. It's not that you have to specify this property, things will work most of the time apart from getting this warning on the console:

Each child in an array should have a unique "key" prop. Check the render method of undefined. By reading the linked documentation it can be easy to not see the implications of this affirmation:

When React reconciles the keyed children, it will ensure that any child with key will be reordered (instead of clobbered) or destroyed (instead of reused). At first it looked to me it was all about performance but, as Paul O’Shannessy pointed, it's actually about identity.

The key here is to understand not everything in the DOM has a representation in React "Virtual DOM" and, because direct manipulations of the DOM (like a user changing an value or a jQuery plugin listening an element) are unnoticed by React, not using unique and constant keys will end up with React recreating the DOM node of a component when the key is not constant (and losing any untracked state in the node) or reusing a DOM node to render another component when the key is not unique (and tying its state to this other component)