A stakeholder is a person interested in a company. If you become CEO of a big company, you'll have to keep the interests of every stakeholder in mind, from the employees to the customers to the investors, whenever you make decisions.
Supposedly people used to gamble by putting their money on a wooden stake, and a person called a stakeholder who wasn't involved in the betting would supervise to make sure everything was fair. No one uses wooden stakes anymore, but we still call the person who holds the money and monitors the betting the stakeholder, and people often use stake to mean "risk," or "investment." That's why someone who is invested in a business is also called a stakeholder.