Walmart is redesigning its lagging Jet.com digital shopping site with more merchandise, faster delivery and a slew of other upgrades in a bid to compete more effectively against Amazon.

Traffic was waning on Jet.com, which Walmart purchased for $3.3 billion roughly two years ago. The site, unlike Walmart.com, primarily targets an affluent, younger crowd living in urban areas like Manhattan in New York.

Jet.com is rolling out a newly redesigned website on Thursday with faster delivery for New York residents. Shoppers will also see more local brands and a more personalized experience that takes into account their zip code or suggests items based on past purchases.

"Our plan is to be more relevant for what you're shopping for," Jet Chief Customer Officer David Echegoyen told CNBC. "Spotify does this really well with music. It gets better the more you use it. And that's the same approach we want to take to retail."

Jet also promises faster delivery for online orders, starting with New York, that aims to rival Amazon-owned Whole Foods, Kroger and Target. Jet will be using its fulfillment center in the Bronx that opens later this fall to help with the rollout.

New Yorkers will be able to order local and craft beer eligible for same-day delivery. And many New York-based residents will soon be able to have groceries delivered within a three-hour window, enabled by Parcel, a logistics company Walmart acquired last year. Previously, there was a cutoff time of 9 a.m. for shoppers to have orders from Jet.com delivered on the same day.

One advantage to being part of the Walmart family today is "having the access to scale" and being able to "bring great prices on groceries to New York," Jet President Simon Belsham told CNBC.

Walmart acquired the business to bring some of Jet's technology, like its "smart-cart" shopping feature that lowers prices based on larger basket sizes, to its own e-commerce platform. Walmart has since been adding more millennial-focused brands from the likes of Lord & Taylor and Moosejaw to its own website.

Jet is also bringing more brands to its website, starting with Nike.

Beginning in October, Nike and Converse merchandise will be available on Jet.com — the companies said "hundreds of products" will go live on the site then, including apparel, sneakers and other workout accessories. Nike merchandise had previously been for sale on Jet.com via third parties. This move mimics a similar one that Jet took in becoming an authorized Apple reseller earlier this year.

"Apple and Nike have both been very good partners to us ... they understood that experiences matter," Echegoyen said.

Marc Lore, the founder of Jet and now president and CEO of Walmart's e-commerce business in the U.S., said the big push in New York in particular for Jet.com "perfectly complements our overall eCommerce portfolio strategy."

Without Walmart stores in Manhattan, Jet.com is viewed by analysts as one way the big-box retailer can still reach those shoppers. And as Belsham alluded to, Jet is still keeping prices low, sticking to Walmart's "everyday low price" mantra.