ESTA is something you fill in that allows you to get on a plane, travel to the US and seek entry on the VWP.
In ye olden days you would be given a form to fill in on the plane, I 94 that was then haded in at Immigration.
Now things are done electronically, the information is part of filing for ESTA, your I 94 assuming admitted can be found online.
One thing I never did but legally you should is have your Passport with you. Like if you have a Green Card you should have it with you, never did that either.