Before saying, "I want to introduce you to a few people whose stories can inspire us in our own growth through mental fitness."
The Duke, who stepped down as a working royal in 2020 and was appointed chief impact officer of the start-up in March 2021, also talked about how he maintains his own mental fitness each day in the clip.
The video shows him interviewing three people, including two-time Olympic gold medal-winning snowboarder Chloe Kim, 22, about their mental health practices while promoting the firm's online life coaching.
Harry also discussed witnessing "trauma", "loss" and grief" on his travels across the globe.
He added: "Throughout the years of travelling around the world, what I saw was the similarities of experiences of trauma, of loss, of grief, of being human."
The Duke said the scenes left him feeling it is "absolutely critical" to "build up resilience" to emotions.
Prince Harry and Meghan are set to appear at a fringe event at the United Nations in New York on Monday, July 18.
The UN confirmed the prince will address an "informal meeting of the plenary to mark the observance of Nelson Mandela Day".
The engagement will be the couple's first public appearance since their brief participation in last month's Platinum Jubilee celebrations for Harry's grandmother, Queen Elizabeth, in London.
The couple made a visit to the UN General Assembly in September 2021 but didn't participate in the speeches at the assembly hall.
Nelson Mandela Day has been celebrated by the UN since 2009 and the public are urged to participate by making a difference in their community.
A post on the United Nations website states: "Everyone has the ability and the responsibility to change the world for the better! Mandela Day is an occasion for all to take action and inspire change."
- Additional reporting by NZ Herald