There are many reasons that people join nonprofit boards. The primary motivation is to do something good for the world. But this post is about the reason that isn't discussed in polite company: "I want to join a board in order to develop business relationships."
Okay, here's the deal: If you just want to make business contacts, there are way easier ways to network than to commit to multiple hours of board and committee meetings, and thousands of dollars. And you will not--I mean really NOT--make a good impression if you merely do the bare minimum, and also start promoting yourself and your business.
Here's how you WILL make a good impression on your fellow board members: by demonstrating your value to the board and organization--with your business acumen, experience, networks and perspectives; your genuine commitment and interest in the mission and people/community you serve (globally, nationally, or regionally); generosity with your time and money; and your leadership. Now that's how to interest people in doing business with you.
The board members that people talk about with admiration and appreciation are the ones who impress people with their value, commitment, and contributions. (Think about the ones you hear and who makes a good impression and why.) These board members also reflect well on their employer companies, so their firms are talked about too. It's the best public relations for a company that is less known or suffering from bad media.
Caveat: This only works if you actually care about the organization's mission. Devoid of personal motivation, people simply fail to appear at meetings or make financial contributions. So that's the key: finding the right match  of candidate to board. When that happens, there's no stopping success--for the board member, the board member's company, the nonprofit, and ultimately the community.