As most Nonprofits are typically founded with the main goal of benefitting the general public, Nonprofits can become "tax exempt" entities. This means that they are free from paying a vast majority of the taxes that are levied on other types of organizations.
However, Nonprofits are not granted tax-exempt status automatically upon formation. After the organization is successfully formed with its state, it must file Form 1023 with the IRS to receive tax exempt status. There may also be some state level filing required to become tax exempt at the state level, depending on where your organization is located.