Board Game Arena

I'm not really understanding Jets...
Do they mean that, for example, I get hit with a two point attack, and if I decide to leave Tokyo, the two point attack doesn't effect me?

Yes that's it

Yup, when you are in Tokyo + attacked, you are offered a choice.
You choose to leave without damage, or stay with damage.

If they only do you 1 point of damage, you can choose to suck it up and stay, or when they hit you with bigger punches, you can safely avoid the damage.