"Big shots" is a colloquialism that essentially means "people in charge" or people who are otherwise really important. The president of a company is a "big shot", for instance.

"Big shot" can be a derogatory way to refer to somebody. The person you're talking about thinks they have power and don't. Another example I can think of for you is the Billy Joel song "Big Shot": "Because you had to be a big shot, didn't you / You had to open up your mouth / You had to be a big shot, didn't you / All your friends were so knocked out" I hope this helped you.