For the most popular packages, it has better documentation and support than commercial alternatives. And it can usually run on less capable hardware - slower processors, less disk space and memory. Less obvious, but perhaps just as important to nonprofits, is the control it offers - not over the source code, but over your message. With open source tools, you need not compromise your values by purchasing from a company whose actions you disagree with. If they are motivated by your mission, they are likely to contribute time and effort for your nonprofit, too.
Open source can be a great source of inexpensive job training.
Nonprofits have time. They have the patience and foresight to develop their own people, where a business would be more inclined to get expertise quickly by buying it from outside. This rule is important whether you use open source software or not. Without a clear purpose, technology projects can quickly spin out of control - or never get off the ground. Find people dedicated first to your mission and second to open source.