The Visa Waiver Program is a program the US has set up that allows most citizens from certain countries to travel to the US for tourism or business up to 90 days without the need for a visa.
To travel on Visa Waiver, each traveler must have Travel Authorization through the Electronic System for Travel Authorization (ESTA) prior to boarding a U.S. bound flight. This is something you can do online at the travel.state.gov website. It will determine your eligibility to travel to the US without a visa.
Keep in mind to travel via Visa Waiver, the reason for your travel must be permitted on a visitor (B1B2 Visa). This is not meant to come to the US with the intent to immigrate, or stay here. It’s purely for short term travel for tourism or business.
Countries in the visa waiver program as of April 16, 2018 are listed below. Citizens from any other country (except Canada and Mexico for which there are special programs), must obtain a visa before entering the United States.
This is the list as of 2018, but it could change. For the latest list, go to travel.state.gov.