Have you ever dated someone based on their future potential? Growth investing is similar(ish). You invest in companies whose earnings or profits are expected to grow at an above average rate compared to others within the same industry. They are often more expensive than other stocks because of their future promise.
It's the opposite of "value investing", where you focus on outright cheap and unloved stocks. As for growth investing sometimes it works, other times, they're still living in their parents' spare room two years later.