A landing page test is a form of MVP testing in which one uses a landing page as a way of gauging some aspect of customer interest and/or purchase intent.
For example, if you are thinking of creating a new solution to solve some problem for a given set of target customers, but want to test the customers' interest and price elasticity before you make key product decisions, you could create a landing page in which you describe your product as though it exists - and then put in a call to action that says "Buy now" or "Learn more". You then send the link to the market place to a targeted list of potential customers who fit criteria for your beachhead market. If enough customers click the call to action, it may validate your hypothesis that there is enough interest. The "Buy now" or "Learn more" could simply lead the customer to a second lead-generation landing page in which their email and/or credit card information is captured and a promise is made to ship them the product when it comes available.
Note that in today's world full of spam and unwanted solicitations, capturing someone's email address is a significant sign of success - the fact that the person willingly provide you with their email address means they probably have a problem similar to or exactly the same as the one you think they have, and they are intrigued by your approach to solving their problem. So capturing an email address is a pretty significant validation point.
Of course the credit card is an even higher bar to clear, so if the customer provides you with their credit card number or paypal information, that is an even better indication of purchase intent - they have effectively opted into a pre-sale situation with you, voting for your product or service with their wallet. This is fantastic validation for your idea.
A landing page test technically is still a qualitative research technique, but it provides quantitative metrics that you can look at relative to email open rate, dwell time on the first landing page, click rate on the call to action and whether they submit their email and/or credit card. Having these metrics means you have a platform to experiment and do more tests. Just be careful with generalizing results from a small sample size - even though the qualitative insights alone are worth the effort.