ESP is an acronym for Email Service Provider.
Just as an ISP provides your internet service, an ESP is the company or service that provides your email account, storage, and ability to send and receive email with others connected to the internet.
Your email may, in fact, be provided by your internet provider, in which case it is acting as both your ISP and ESP. On the other hand, many free email services, such as Outlook.com, Yahoo! Mail, and Google Mail are all acting simply as email providers, and thus qualify as ESPs.