Let's say we want to console.log each time the component mounts:

hocLogger.js

export default function hocLogger(Component) {
  return class extends React.Component {
    componentDidMount() {
      console.log('Hey, we are mounted!');
    }
    render() {
      return <Component {...this.props} />;
    }
  }
}

Use this HOC in your code:

MyLoggedComponent.js

import React from "react";
import {hocLogger} from "./hocLogger";

export class MyLoggedComponent extends React.Component {
    render() {
        return (
            <div>
                This component get's logged to console on each mount.
            </div>
        );
    }
}

// Now wrap MyLoggedComponent with the hocLogger function 
export default hocLogger(MyLoggedComponent);

Let's say we have a component that should only be displayed if the user is logged in.

So we create a HOC that checks for the authentication on each render():

AuthenticatedComponent.js

import React from "react";

export function requireAuthentication(Component) {
    return class AuthenticatedComponent extends React.Component {

        /**
         * Check if the user is authenticated, this.props.isAuthenticated
         * has to be set from your application logic (or use react-redux to retrieve it from global state).
         */
        isAuthenticated() {
            return this.props.isAuthenticated;
        }

        /**
         * Render
         */
        render() {
            const loginErrorMessage = (
                <div>
                    Please <a href="/login">login</a> in order to view this part of the application.
                </div>
            );

            return (
                <div>
                    { this.isAuthenticated === true ? <Component {...this.props} /> : loginErrorMessage }
                </div>
            );
        }
    };
}

export default requireAuthentication;

We then just use this Higher Order Component in our components that should be hidden from anonymous users:

MyPrivateComponent.js

import React from "react";
import {requireAuthentication} from "./AuthenticatedComponent";

export class MyPrivateComponent extends React.Component {
    /**
     * Render
     */
    render() {
        return (
            <div>
                My secret search, that is only viewable by authenticated users.
            </div>
        );
    }
}

// Now wrap MyPrivateComponent with the requireAuthentication function 
export default requireAuthentication(MyPrivateComponent);

This example is described in more detail here.