Can I update a component's props in React.js?

After starting to work with React.js, it seems like props are intended to be static (passed in from the parent component), while state changes based upon events. However, I noticed in the docs a reference to componentWillReceiveProps, which specifically includes this example:

componentWillReceiveProps: function(nextProps) {
  this.setState({
    likesIncreasing: nextProps.likeCount > this.props.likeCount
  });
}

This seems to imply that the properties CAN change on a component based upon the comparison of nextProps to this.props. What am I missing? How do props change, or am I mistaken about where this gets called?

A component cannot update its own props unless they are arrays or objects (having a component update its own props even if possible is an anti-pattern), but can update its state and the props of its children.

For instance, a Dashboard has a speed field in its state, and passes it to a Gauge child thats displays this speed. Its render method is just return <Gauge speed={this.state.speed} />. When the Dashboard calls this.setState({speed: this.state.speed + 1}), the Gauge is re-rendered with the new value for speed.

Just before this happens, Gauge's componentWillReceiveProps is called, so that the Gauge has a chance to compare the new value to the old one.

PROPS

A React component should use props to store information that can be changed, but can only be changed by a different component.

STATE

A React component should use state to store information that the component itself can change.

A good example is already provided by Valéry.