The video discusses a common trait among billionaires, which is their relentless pursuit of goals. They are described as being like 'a dog with a bone,' meaning once they focus on a goal, they persistently pursue it without giving up. This relentlessness is only limited by the laws of physics. The speaker emphasizes that billionaires challenge conventional limits by asking why something can't be done, such as hiring 100 people in three days, and then finding ways to overcome those obstacles. This mindset of questioning and overcoming perceived barriers is what sets them apart and drives their success.