If you are from the UK or one of the other countries that is a part of the US Visa Waiver Program and you want to travel to the United States for a holiday or for a business trip then you will need to have an ESTA before you board the plane. The ESTA replaces the paper cards that people used to fill out while they were on the plane itself.
The ESTA is not a visa. Rather, it is a form of verification that people go through before they travel. The distinction is important because some people will still need a Visa as well.
There is a nominal fee for applying for an ESTA via the government website. Once you have had your ESTA approved, it will be valid for two years, or until the passport that it is associated with expires (whichever of those comes first). You can take more than one trip on the same ESTA. There is no need to re-apply as long as your ESTA is still valid.
You should make sure that you apply via the DHS.gov website. There are other third party websites, some of which look quite convincing, which offer to help people complete the application process. There is no need to use those sites. The form that you fill out on the official website is quite simple, and it should take no more than 20 minutes to complete it.
The US Embassy can help you if you have any questions about the ESTA, whether you can travel under the Visa Waiver Program, and whether you will need a visa. You can get preliminary help on their website, and call them for more detailed information if your circumstances complex. Make them your first port of call if you need advice about how to get a visa or ESTA.