The board of directors of ExxonMobil Corp. includes the CEOs of Xerox, Travelers, Merck, and Caterpillar, and the former CEOs of IBM, Nestle, Pepsi, and Johnson & Johnson. In contrast, the board of directors of a new startup might consist solely of its founder: a 20-something first-time entrepreneur. Both serve the same purpose, which is to represent the rights and viewpoints of shareholders. A company's board of directors is elected by the company's shareholders, so before a startup receives outside funding, the board is "elected" by--and usually consists of--the founders (although for a tiny company with one or two founders, "the board" may exist in name only).
Once a company receives its initial funding, there are now other owners of the company in addition to the founders. Where it gets tricky is that all of a company's shareholders can voluntarily agree to sign a Shareholders Agreement in which they all agree to cast their votes in a certain way. So for a startup company that has taken in an investment from angel investors or venture capitalists, the Shareholders Agreement might provide that the company will have a board of directors consisting of three people, and, regardless of how many shares anyone has, everyone agrees to vote for one director nominated by the company's founders, one director nominated by the investors, and one "outside" director that everyone can agree on. So in this case, even though the founder still owns 80% of the company, the investors have an equal voice when it comes to control.
In a larger startup, perhaps after one or two investment rounds have taken place, the board might be expanded to five people, with two directors chosen by the common stockholders (the founders), two by the investors (for example, by the directors of venture capital funds that might have invested in the business, or by the most important angel investor, if any), and one independent director agreed to by everyone.
If, at this point, the company has a non-founder CEO, that position might get a board seat (with one for the founders). And if there's only one major investor, they may choose to fill one of their two seats with an industry expert.
But, typically, the common seats will be filled by the founder(s); the investor seats by the lead angel (for an angel deal) or the venture capital partner and/or an associate (for a venture-led deal); and the independent seat(s) by someone experienced and knowledgeable, and who is acceptable to...