What it means
When someone gets a little bit of authority and completely overdoes it, throwing orders around just because they can. Being on a power trip is less about the job and more about enjoying the feeling of bossing people.
Usage examples
"The new prefect's on a right power trip, confiscating phones and writing names down like it's a police state."
"Ever since he got the clipboard he has been on a total power trip."
"The new supervisor is on a power trip, writing people up for nothing."
"Give him a lanyard and five minutes, and he's straight on a power trip telling everyone where they can stand."
"She's been on such a power trip since they made her shift lead, acting like asking for a break is a federal crime."
Where it comes from
This one grew out of the older drug sense of trip, meaning an intense headspace or altered state. Pair that with power and you get somebody getting a little taste of authority, then floating off on the ego-fizz of bossing people about. It’s been around in everyday English since the late 20th century.