New York Design Week always inundates the city with sumptuous materials and one-of-a-kind objets — coffee tables made of imported marble, custom lamps with brass hardware and sofas upholstered in wool. But “OUTSIDE/IN,” a show at Lyle Gallery on the Lower East Side, offers something more, with pieces that lean into the makers’ heritage and backgrounds. Lighting fixtures are inspired by the Indian tradition of hair oiling, a chair is meant to soothe anxiety and wall art is made of construction materials tied to a childhood memory. Here, the stories are what matter.

“Everything has some sort of background to it, or it has layers and guts to it. It’s not living just to be a fancy-ass chair for rich people,” said Lin Tyrpien, who co-curated the show with Jenny Nguyen, the founder of the public relations company Hello Human.

Now in its 13th year, the annual NYCxDESIGN Festival brings together designers and manufacturers to exhibit new furnishings and home décor, with events taking place all over the city. On view through June 1, the show at Lyle Gallery features 12 designers, most of whom are emerging. The gallery held an open call for furniture makers and artists, which received over 200 submissions, through which Ms. Tyrpien and Ms. Nguyen selected the works to be featured. The designers come from across the globe, including Senegal, Nigeria, India and more.

Ms. Tyrpien, who is a co-owner of the gallery, said that the recent anti-D.E.I. movements have been another impetus for the show. “With funding being gone from a lot of D.E.I. initiatives, what a timely thing to be combating that,” she said.

Here’s a look at some of the designers in the show and the stories behind their work.

The interviews below have been lightly edited for length and clarity.