How can something be greater than $100\%$?

Say 1 out of 10 people quit in year 1. Now if 4.5 out of 10 people quit in year 2 it is up 350%. Does this make sense? The percentages compare numbers relative to each other.

$100$% of something means all of it.

$200$% of the same thing means twice as much.

$350$% means $3.5$ times the original amount.

$\%$ (percent) literally means "over 100".

So when people say "$350\%$ more likely to quit", what they loosely mean is that, if $x$ is how many people (usually) quit, then $x + 3.5x$ represents how many people will quit in this new scenario.

Your question "how can it be bigger than 100%" suggests that you are thinking about probabilities which never go higher than 1. But that's because of its definition and the fact that people frequently use percentages to represent probabilities.