I am on the board of directors of a 501c3 corporation. Another member of our board wants to have our website post a link to her website which is a for profit business. I have a problem with this because she is trying to profit her business from our website. Is this legal?

Legal, yes, ethical no.

On a side note, may I suggest you be more careful reading instructions. You originally posted this in the Introductions forum which is clearly marked as not the place to ask questions, but just to introduce yourself.

Thank you very much for the prompt response. Your answer was very helpful.

I am president of a 501C3 Corp, and the web site can link to many different things, some link to places like goggle search, ( for advertising dollars) they may have links to Amazon books and other places.

So yes they can, but it would be expected to perhaps charge advertising for the link perhaps or set up a page for everyone's personal or business links.