Well you're talking about two related but different pieces of data:
1. Demand/Market for a solution to a given problem
2. How well you've achieved product-market-fit with your particular solution.
Determining #1 is fairly straightforward:
A. Google searches for a given query (unmet need)
B. Chatter about that problem or other solutions (buzz)
C. Competitors selling products in that vertical (precedent)
D. Competitors bidding on keywords related to that vertical
Determining #2 is harder / more nuanced; and to a certain extent is a fruitless endeavor until you've hit significant sample sizes. The first 10 people you try to sell might say no, that doesn't mean the product is wrong for the market; that could just be random chance. The only sure-fire way to test product-market fit is to get your product in front of a statistically significant number of users, and see if they bite.
I use the term "bite" because I don't mean "convert". Optimizing your conversion process (getting users to actually sign up / purchase, etc) takes time and that comes later. In the beginning all you need to test is if they care about your product at all (are engaged when presented the idea). That's where the field of engagement analytics comes into play, and that's a big subject...but hopefully I've pointed you in a useful direction.