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.
Spoiler alert: a letter of intent is not the same as a cover letter. They're similar (being letters and all, and focused on yourself), but are actually used in different situations. Your cover letter is what you write when you're applying to a specific job you found through traditional channels (online job search, referral, recruiter). It details why you're a great fit for this particular job. A letter of intent is what you write when you're cold-calling (leaving a resume without being solicited for one), or applying for a job in a more general situation, like a job fair or submitting your resume to a general pool. The letter of intent is similar in that you're selling yourself, but tends to be less granular about a particular position. Letters of intent are often more networking-related, or aspirational, than position-oriented. Because you may have fewer specifics in hand about what you're applying for and who will be reading your application package, it's likely you won't have the most personalized opener. That's okay! Be general, but professional, formal, and polite.