This agreement is most often used in transactions involving a purchase. Sometimes two parties will know that they want to do a business deal together, but they aren't ready to sign an actual agreement. For example, they may agree that one party will sell his or her business for a certain price, but they do not yet agree on who will take on certain liabilities of the business. The parties can sign this document to show each other a good faith intention to work out a deal. It can also help parties get on the same page as to what they expect from the purchase.
In the bad example, Jean is too vague, and has a few red flags, like suggesting that her last job didn't end well, and making an inappropriate joke about Scorpios to gloss it over. You can tell people you're great, but it's better to prove it by offering specifics, like she does in the better example. In the second example, Jean's letter body is more clearly organized, and makes sure to give the most relevant details about her career so far.