This term is mostly used when referring to business enterprises. If something is financially viable it means that it has a higher than not likelihood of success from an economic or business perspective (i.e. they have the funds necessary to succeed or they have a business model likely to succeed). I've most commonly heard the term used when referring to something's future performance, as in:
"His proposal is not financially viable. I predict that his business will fail within the first year."
Hope this helps!