A Letter of Intent is a written document that outlines a preliminary agreement between two parties regarding the terms of a potential purchase or other transaction. The two parties can settle on certain terms while agreeing to continue to negotiate the other terms and details of the transaction before actually signing a purchase agreement.
As with any professional correspondence, you don't want to seem too stiff or formal, like you're writing a letter from a Victorian template or a bad spam email asking someone to send money to a deposed prince overseas—but you also don't want to be too conversational. You're not in a dialogue yet, so it's important to treat this like a professional first interaction, and not like you're skipping several steps and asking to meet for coffee. The tone you're reaching for is, "You don't know me yet, but I'm interested in your company and want to tell you more about why."