Many small businesses, especially one-person businesses, don't see the point in investing the time, work and money in creating a brand identity. After all, they're very good at whatever it is that they do, and they should be able to make more than "just a living" by simply putting up a website, being themselves, and delivering a high-quality service, right?
Unfortunately, it doesn't usually work out that smoothly. And that's because of customer reluctance.
Most of the one-person businesses that I work with are service businesses. They charge a fair amount for their services – an hourly or project amount that allows them to pay the rent/mortgage, to put gas in their car (which is not a laughing matter in today's economy in the United States!), to eat and have fancy coffees, etc. Which means that when a customer wants to work with them, it usually means that they have to hand over a not-inconsequential pile of money.
Many people are just plain reluctant to hand this amount of money over to a person they've just met – no matter how nice their suit is, or how well their resume reads.
Your brand's main job is to act as the face of your business. What this means is that instead of you being the main focus when your customers go to pay you, the brand takes some of the weight off your shoulders. Instead of giving their pile of hard-earned money to "Sue", they make their check out to "Trust-Worthy Consulting, LLC". And, your brand identity gives them another visual connection to make with your business aside from your face. This is a lot easier for many customers to deal with.
A brand also has many trust-building characteristics – by having business materials that look professional, you're basically reassuring your potential customers that you're not planning to take their money and run off. In other words, a brand identity makes your business look established and stable, and less risky to do business with.