• Zillow's challenge is turning the millions of people who dreamily browse its website into actual homebuyers, CEO Rich Barton told CNBC on Thursday.
• The online real estate marketplace saw a 19% increase in visitors to its website and app in 2020 during the pandemic.
• "We monetize a single-digit percentage of the people that come visit us right now," Barton said.

Zillow CEO Rich Barton told CNBC on Thursday the company hopes to turn the wave of people who dreamily browsed its website last year into actual homebuyers.

Zillow has long been associated with so-called "real estate porn," Barton acknowledged in a "Squawk on the Street" interview. He noted a headline in a San Francisco newspaper in 2006 made the comparison shortly after Zillow launched.

It's an association that took off during the coronavirus pandemic. Many people turned to Zillow with the legitimate purpose of buying a home, evidenced by the company's 22% revenue growth in 2020. But another cohort emerged and turned to Zillow for a sort of pandemic escapism, perhaps searching for a dream home in a new city even though moving there wasn't a realistic possibility.

Indeed, Zillow saw a 19% increase in traffic to its website and app in 2020 with 9.6 billion visitors, and the whole notion of fantasizing about homes on Zillow was made fun of last week on NBC's "Saturday Night Live."

"People have been on this for quite some time. What's wildly gratifying and exciting for me and our team is to break through a cultural barrier into this really rare air where 'Saturday Night Live' is spoofing it," said Barton, a co-founder of Zillow.

Of the billions of visits to the company's website and app, Barton said a "very low" percentage of them turn directly into a sale through Zillow. "But that's OK, because we get 9.6 billion of them."

To be sure, that doesn't mean Zillow plans to let its cultural cache go to waste, Barton said. He likened a first-time visitor to Zillow to being at the top of a funnel while a home sale is like making it to the bottom. "Our challenge is ... to increasingly turn more of that shopping and dreaming traffic into transactions," he said.

"We monetize a single-digit percentage of the people that come visit us right now," added Barton. "That's potential energy for us that should fuel our growth for many years to come."

Investors have been betting Zillow's best days are ahead of it. The company's stock hit an all-time high Thursday of $205.70 per share, one day after the company released quarterly results.

Zillow reported adjusted Q4 earnings of 41 cents per share on revenue of nearly $789 million, both of which beat expectations. While fourth-quarter revenue dropped 16% from the year-ago period, Zillow's full-year 2020 revenue of $3.34 billion rose 22% compared with 2019 as the housing market heated up during the coronavirus pandemic. Zillow also issued rosy guidance on first-quarter revenue.

Shares of Zillow, which were up around 280% in the past 12 months, soared about 15% on Thursday.

Tiffany McGhee, a Zillow shareholder, said Thursday on CNBC's "Halftime Report" that she liked the stock as a continued play on digitization of the real estate market.

"I love this idea of 'real estate porn,' kind of like this byproduct of Zillow," said McGhee, CEO and CIO of Pivotal Advisors. "What they're trying to do is take this funnel of dreamers and make them buyers, and all they need to do is get this 9.6 billion [visitors] to keep coming back. That's what they're doing. ... There really is this kind of revolution going on, and that's what I'm invested in."

Disclosure: NBCUniversal is the parent company of CNBC and NBC, which broadcasts "Saturday Night Live." Tiffany McGhee also serves as a CNBC contributor.