When you're building a new products, user feedback is critical. You can gather feedback in a variety of ways, through in-person customer development interviews, surveys, and by simply looking at the data. I'm particularly fond of doing user testing (UserTesting is an awesome tool for this) although its only a "simulation" of what your users are actually doing.
FullStory captures a screen recording of your site visitor's actions and behavior within (cue Steve Irwin impression) their natural environment. We've used it many times at Product Hunt to better understand how people are using new or beta features we're building. It's 👍🏼.
They do one thing instead of many, and they do it well, but the pricing model didn't work all that well for us. Besides, it's still one step behind Amplitude and the likes in terms of seeing the customer journey. I would still recommend them for the search function.